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8th Maths 6.3

Chapter 6 Squares and Square Roots NCERT Class 8th solution of Exercise 6.1 NCERT Class 8th solution of Exercise 6.2 NCERT Class 8th solution of Exercise 6.4 Exercise 6.3

$text {Square root you must learn.}$

$1^2=sqrt{1}=1$

$2^2=sqrt{4}=2$

$3^2=sqrt{9}=3$

$4^2=sqrt{16}=4$

$5^2=sqrt{25}=5$

$6^2=sqrt{36}=6$

$7^2=sqrt{49}=7$

$8^2=sqrt{64}=8$

$9^2=sqrt{81}=9$

$10^2=sqrt{100}=10$

$11^2=sqrt{121}=11$

$12^2=sqrt{144}=12$

$13^2=sqrt{169}=13$

$14^2=sqrt{196}=14$

$15^2=sqrt{225}=15$

$16^2=sqrt{256}=16$

$17^2=sqrt{289}=17$

$18^2=sqrt{324}=18$

$19^2=sqrt{361}=19$

$20^2=sqrt{400}=20$

$21^2=sqrt{441}=21$

$22^2=sqrt{484}=22$

$23^2=sqrt{529}=23$

$24^2=sqrt{756}=24$

$25^2=sqrt{625}=25$

$26^2=sqrt{676}=26$

$27^2=sqrt{729}=27$

$28^2=sqrt{224}=28$

$29^2=sqrt{841}=29$

$30^2=sqrt{900}=30$

$31^2=sqrt{961}=31$

$32^2=sqrt{1024}=32$

$33^2=sqrt{1089}=33$

$34^2=sqrt{1156}=34$

$35^2=sqrt{1225}=35$

$36^2=sqrt{1296}=36$

$37^2=sqrt{1369}=37$

$38^2=sqrt{1444}=38$

$39^2=sqrt{1521}=39$

$40^2=sqrt{1600}=40$ `41^2=sqrt{1...

Chapter 6 Squares and Square Roots NCERT Class 8th solution of Exercise 6.1 NCERT Class 8th solution of Exercise 6.3 NCERT Class 8th solution of Exercise 6.4 Exercise 6.2 Q1. Find the square of the following numbers. i)

$32$ ii)

$35$ iii)

$86$ iv)

$93$ v)

$71$ vi)

$46$

$text{Sol.}$ i)

$32^2$

$= (30 + 2)^2$

$= 30(30 + 2) + 2(30 + 2)$

$= 30^2 + 30 times 2 + 2times 30 + 2^2$

$= 900 + 60 + 60 + 4$

$= 1024$

$text{Answer:}$

$1024$ . ii)

$35^2$

$= (30 + 5)^2$

$= 30(30 + 5) + 5(30 + 5)$

$= 30^2 + 30times5 + 5times30 + 5^2$

$= 900 + 150 + 150 + 25$

$= 1225$

$text{Answer:}$

$1225$ . iii)

$86^2$

$= (80 + 6)^2$

$= 80(80 + 6) + 6(80 + 6)$

$= 80^2 + 80times6 + 6times80 + 6^2$

$= 6400 + 480 + 480 + 36$

$= 7396$

$text{Answer:}$

$7396$ . iv)

$93^2$

$= (90 + 3)^2$

$= 90(90 + 3) + 3(90 + 3)$

$= 90^2 + 90times3 + 3times90 + 3^2$

$= 8100 + 270 + 270 + 9$

$= 8649$

$text{Answer:}$

$8649$ . v)

$71^2$

$= (70 + 1)^2$

$= 70(70 + 1) + 1(70 + 1)$

$= 70^2 + 70times1 + 1times70 + 1^2$

$= 4900 + 70 + 70 + 1$

$= 5041$ `t...

8th Maths 6.1

Chapter 6 Squares and Square Roots NCERT Class 8th solution of Exercise 6.2 NCERT Class 8th solution of Exercise 6.3 NCERT Class 8th solution of Exercise 6.4 Exercise 6.1

$text {Square you must learn.}$

$1^2=1$

$2^2=4$

$3^2=9$

$4^2=16$

$5^2=25$

$6^2=36$

$7^2=49$

$8^2=64$

$9^2=81$

$10^2=100$

$11^2=121$

$12^2=144$

$13^2=169$

$14^2=196$

$15^2=225$

$16^2=256$

$17^2=289$

$18^2=324$

$19^2=361$

$20^2=400$

$21^2=441$

$22^2=484$

$23^2=529$

$24^2=756$

$25^2=625$

$26^2=676$

$27^2=729$

$28^2=224$

$29^2=841$

$30^2=900$

$31^2=961$

$32^2=1024$

$33^2=1089$

$34^2=1156$

$35^2=1225$

$36^2=1296$

$37^2=1369$

$38^2=1444$

$39^2=1521$

$40^2=1600$

$41^2=1681$

$42^2=1764$

$43^2=1849$

$44^2=1936$

$45^2=2025$

$46^2=2116$

$47^2=2209$

$48^2=2304$

$49^2=2401$

$50^2=2500$ Q1. what will be the unit digit of the squares of the following numbers? i)

$81$ ii)

$272$ iii)

$799$ iv)

$3853$ v)

$1234$ vi)

$26387$ vii)

$52698$ viii)

$99880$ ix)

$12796$ x)

$55555$

$text{Sol:}$ i)

$text{The unit digit of 81 is 1,}$ `text{ so tha...

NCERT Class 10th solution of Exercise 12.1 NCERT Class 10th solution of Exercise 12.2 NCERT Class 10th solution of Exercise 13.1 NCERT Class 10th Maths Projects Exercise 12.3 Q1. Find the area of the shaded region in Figure, if

$text{PQ = 24 cm, PR = 7 cm}$ and

$text{O}$ is the centre of the circle.

$text{Sol.}$

$text{In right}triangle text{QPR by Pythagoras theorem.}$

$text{RQ = }sqrt((text{PQ})^2 + (text{RP})^2)$

$= sqrt((24)^2+(7)^2)$

$= sqrt(576 + 49)$

$= sqrt(625)$

$= 25$

$text{r} = 25/2$

$text{Area of semicircle QPR = }1/2 pi text{r}^2$

$= 1/2 times 22/7 times(25/2)^2$

$= (11 times 625)/28$

$= 6875/28 text{ cm}^2$

$text{Area of right }triangle text{RPQ} = 1/2 times RP times PQ$

$= 1/2 times 7 times 24$

$= 84 text{ cm}^2$

$text{Area of the shaded region =}$

$text{ ar of semicircle QPR - ar of }triangle text{RPQ}$

$= 6875/28 - 84$

$= (6875 - 2352)/28$

$= 4523/28 text{ cm}^2$

$text{Answer}$

$text{The area of shaded region is } 4523/28 text{ cm}^2$ .

NCERT Class 10th solution of Exercise 12.1 NCERT Class 10th solution of Exercise 12.3 NCERT Class 10th Maths Projects Exercise 12.2 Unless stated otherwise, use

$pi = 22/7$ . Q1. Find the area of a sector of a circle with radius

$text{6 cm}$ if angle of the sector is

$60^circ$ .

$text{Sol.}$

$text{Area of sector = }theta/{360^circ}times pi text{r}^2$

$text{ = }60^circ/{360^circ}times 22/7 times(6)^2$

$text{ = }(6times6)/6times22/7$

$text{ = }(6times22)/7$

$text{ = } 132/7text{ cm}^2$

$text{Answer}$

$text{Area of sector }132/7 text{ cm}^2.$

NCERT Class 10th solution of Exercise 12.3 NCERT Class 10th solution of Exercise 12.2 NCERT Class 10th Maths Projects Exercise 12.1 Unless stated otherwise, use

$pi = 22/7$ . Q1. The radii of two circles are

$text{19 cm}$ and

$text{9 cm}$ respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.

$text{Sol.}$

$text{circumference of big circle}$

$text{= circumference of}$ (

$text{circle}_1$ +

$text{circle}_2$ ) 2

$pi$

$text{R}$ = 2

$pi$

$text{r}_1$ + 2

$pi$

$text{r}_2$ 2

$pi$

$text{R}$ =

$2$

$pi$ {

$19 + 9$ }

$text{R}$ =

$28$

$text{cm.}$

$text{Answer :}$

$text{Radius}$ =

$28$

$text{cm.}$

8th Maths 7.1

Chapter 7 Cubes and Cube Roots NCERT Class 8th solution of Exercise 7.2 Exercise 7.1

$text {Cube you must learn}$

$1^3=1$

$2^3=8$

$3^3=27$

$4^3=64$

$5^3=125$

$6^3=216$

$7^3=343$

$8^3=512$

$9^3=729$

$10^3=1000$

$11^3=1331$

$12^3=1728$

$13^3=2197$

$14^3=2744$

$15^3=3375$

$16^3=4096$

$17^3=4913$

$18^3=5832$

$19^3=6859$

$20^3=8000$ Q1. Which of the following numbers are not perfect cubes? i)

$216$ ii)

$128$ iii)

$1000$ iv)

$100$ v)

$46656$

$text{Sol.}$ i)

$text{Prime factorisations of}$

$216=underline(2times2times2)times underline(3times3times3)$

$text{Answer:}$

$text{216 is the perfect cube.}$ ii)

$text{Prime factorisations of}$

$128=underline(2times2times2)times underline(2times2times2)times2$

$text{Answer:}$

$text{128 is not perfect cube}$ iii)

$text{Prime factorisations of}$

$1000=underline(2times2times2)times underline(5times5times5)$

$text{Answer:}$

$text{1000 is perfect cube}$ iv)

$text{Prime factorisations of}$

$100=underline(2times2)timesunderline(5times5)$

$text{Answer:}$ `text{1...

8th Maths 7.2

Chapter 7 Cubes and Cube Roots NCERT Class 8th solution of Exercise 7.1 Exercise 7.2

$text {Cube Roots you must learn}$

$root [3]{1}=1$

$root [3]{8}=2$

$root [3]{27}=3$

$root [3]{64}=4$

$root [3]{125}=5$

$root [3]{216}=6$

$root [3]{343}=7$

$root [3]{512}=8$

$root [3]{729}=9$

$root [3]{1000}=10$

$root [3]{1331}=11$

$root [3]{1728}=12$

$root [3]{2197}=13$

$root [3]{2744}=14$

$root [3]{3375}=15$

$root [3]{4096}=16$

$root [3]{4913}=17$

$root [3]{5832}=18$

$root [3]{6859}=19$

$root [3]{8000}=20$ Q1 Find the cube root of each of the following numbers by prime factorisation method. i)

$64$ ii)

$512$ iii)

$10648$ iv)

$27000$ v)

$15625$ vi)

$13824$ vii)

$110592$ viii)

$46656$ ix)

$175616$ x)

$91125$

$text{Sol.}$ i)

$text{Prime factorisations of}$

$root [3]{64} = underline(2times2times2)times underline(2times2times2)$

$=2times2$

$=4$

$text{Answer:}$

$text{The cuberoot of 64 is 4.}$ ii)

$text{Prime factorisations of}$ `root [3]{512} =underline(2times2times2)times underline(2times2times2)times und...

NCERT Class 8th solution of exercise 3.1 NCERT Class 8th solution of Exercise 3.2 NCERT Class 8th solution of Exercise 3.4 Exercise 3.3 Q1. Given a parallelogram

$text{ABCD}$ . Complete each statement with the definition or property used. i)

$text{AD}$ = .......... ii)

$angle text{DCB}$ = ............ iii)

$text{OC}$ = ........... iv)

$m angle text{DAB} + m angletext{CDA}$ = ..........

$text{Answer:}$ i)

$text{BC (Opposite sides are equal)}$ ii)

$angletext{DAB (Opposite angles are equal)}$ iii)

$text{OA (Diagonals bisect each other)}$ iv)

$180^circ text{(Interior opposite angles,}overline text{AB}∥ overline text{DC})$

NCERT Class 8th solution of Exercise 3.1 NCERT Class 8th solution of Exercise 3.3 NCERT Class 8th solution of Exercise 3.4 Exercise 3.2 Q1. Find the following figures. a)

$text{Sol.}$

$text{We know that}$

$text{Sum of the external angles of a polygon is }360^circ.$

$text{x }+125^circ+125^circ = 360^circ$

$text{x} = 360^circ - 250^circ$

$text{x} = 110^circ$

$text{Answer:}$

$text{x} = 110^circ$ . b)

$text{Sol.}$

$text{We know that}$

$text{Sum of the external angles of a polygon is }360^circ.$

$text{x }+90^circ+60^circ+90^circ+70^circ = 360^circ$

$text{x} = 360^circ - 310^circ$

$text{x} = 50^circ$

$text{Answer:}$

$text{x} = 50^circ$

NCERT Class 8th solution of Exercise 3.2 NCERT Class 8th solution of Exercise 3.3 NCERT Class 8th solution of Exercise 3.4 NCERT Class 8th solution of Exercise 2.1 Exercise 3.1 Q1. Given here are some figures. Classify each of them on the basis of the following. a) Simple curved b) Simple closed curved curve c) Polygon d) Convex polygon e) Concave polygon

$text{Answer:}$ a)

$1, 2, 5, 6, 7$ b)

$1, 2, 5, 6, 7$ c)

$1, 2$ d)

$2$ e)

$1$

NCERT Class 8th solution of Exercise 3.1 NCERT Class 8th solution of Exercise 3.2 NCERT Class 8th solution of Exercise 3.3 Exercise 3.4 Q1. State whether True or False. a) All rectangles are squares b) All rhombuses are parallelograms c) All squares are rhombuses and also rectangles d) All squares are not parallelograms e) All kites are rhombuses f) All rhombuses are kites g) All parallelograms are trapeziums h) All squares are trapeziums.

$text{Answer:}$ a)

$text{false,}$ b)

$text{true,}$ c)

$text{true,}$ d)

$text{false,}$ e)

$text{false,}$ f)

$text{true,}$ g)

$text{true,}$ h)

$text{true.}$

Chapter 2 Linear Equations in One Variable NCERT Class 8th solution of Exercise 2.1 NCERT Class 8th solution of Exercise 2.2 NCERT Class 8th solution of Exercise 2.3 NCERT Class 8th solution of Exercise 2.5 NCERT Class 8th solution of Exercise 2.6 Exercise 2.4 Q1. Amina thinks of a number and subtracts

$5/2$ from it. She multiplies the result by

$8$ . The result now obtained is

$3$ times the same number she thought of. What is the number?

$text{Sol.}$

$text{Let Amina thinks of a number is x}$

$text{According to question}$

$(text{x} - 5/2)times8 = 3 times text{x}$

$text{8x - 20 = 3x}$

$text{8x - 3x = 20}$

$text{5x = 20}$

$text{x} = 20/5$

$text{x} = 4$

$text{Answer:}$

$text{The number is 4.}$

8th Maths 2.2

Chapter 2 Linear Equations in One Variable NCERT Class 8th solution of Exercise 2.1 NCERT Class 8th solution of Exercise 2.3 NCERT Class 8th solution of Exercise 2.4 NCERT Class 8th solution of Exercise 2.5 NCERT Class 8th solution of Exercise 2.6 Exercise 2.2 Q1. If you subtract

$1/2$ from a number and multiply the result by

$1/2$ , you get

$1/8$ . What is the number? Solution : Let a number be

$x$ According to question

$(x-1/2)times1/2=1/8$ Multiply

$2$ on both sides.

$(x-1/2)times1/2times2=1/8times2$

$x-1/2=1/4$ Add

$1/2$ on both sides

$x-1/2+1/2=1/4+1/2$

$x=(2+4)/4times2$

$x=6/8$

$x=3/4$ Answer : The number is

$3/4$ .

8th Maths 2.6

Chapter 2 Linear Equations in One Variable NCERT Class 8th solution of Exercise 2.1 NCERT Class 8th solution of Exercise 2.2 NCERT Class 8th solution of Exercise 2.3 NCERT Class 8th solution of Exercise 2.4 NCERT Class 8th solution of Exercise 2.5 Exercise 2.6 Solve the following equations. Q1.

$text{8x - 3}/text{3x} = 2$

$text{Sol.}$

$text{8x - 3}/text{3x} = 2$

$text{8x - 3} = text{3x} times 2$

$text{8x - 3 = 6x}$

$text{8x - 6x = 3}$

$text{2x} = 3$

$text{x} = 3/2$

$text{Answer:}$

$text{x} = 3/2$

8th Maths 2.5

Chapter 2 Linear Equations in One Variable NCERT Class 8th solution of Exercise 2.1 NCERT Class 8th solution of Exercise 2.2 NCERT Class 8th solution of Exercise 2.3 NCERT Class 8th solution of Exercise 2.4 NCERT Class 8th solution of Exercise 2.6 Exercise 2.5 Solve the following linear equations. Q1.

$text{x}/2 - 1/5 = text{x}/3 + 1/4$

$text{Sol.}$

$text{x}/2 - 1/5 = text{x}/3 + 1/4$

$text{x}/2 - text{x}/3 = 1/4 + 1/5$

$text{3x - 2x}/6 = (5 + 4)/20$

$text{x}/6 = 9/20$

$text{x} = (6 times 9)/20$

$text{x} = (3 times 9)/10$

$text{x} = 27/10$

$text{Answer:}$

$text{x} = 27/10$ .

8th Maths 2.3

Chapter 2 Linear Equations in One Variable NCERT Class 8th solution of Exercise 2.1 NCERT Class 8th solution of Exercise 2.2 NCERT Class 8th solution of Exercise 2.4 NCERT Class 8th solution of Exercise 2.5 NCERT Class 8th solution of Exercise 2.6 Exercise 2.3

$text{Solve the following equations and}$

$text{check your results.}$ Q1.

$text{3x = 2x + 18}$

$text{Solution:}$

$text{3x = 2x + 18}$

$text{3x - 2x = 18}$

$text{x = 18}$

$text{Check the result}$

$3times18 = 2times18 + 18$

$54 = 36 + 18$

$54 = 54$

$text{Answer:}$

$text{x = 18.}$

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8th Maths 6.3

8th Maths 6.2

8th Maths 6.1

10th Maths 12.3

10th Maths12.2

10th Maths 12.1

8th Maths 7.1

8th Maths 7.2

8th Maths 3.3

8th Maths 3.2

8th Maths 3.1

8th Math 3.4

8th Maths 2.4

8th Maths 2.2

8th Maths 2.6

8th Maths 2.5

8th Maths 2.3