Blue ray books class 8 maths solution chapter square and square root

Square and Square root

EXERCISE (A)

 

1.Write the unit’s digits of the squares of the following numbers.

(a) 93

(b) 72

(c) 546

(d) 931

2.Without actual squaring find the value of:

(a) \( 22^2-21^2 \)

(b)\( 685^2-684^2 \)

(c) \( 108^2-107^2 \)

3.Which of the following numbers are the squares of odd numbers.

(a) 9

(b) 225

(c) 1089

(d) 7395

4.Which of the following numbers are the squares of even number.

(a) 64

(b) 441

(c) 792

(d) 2952

5.Find the squares of the following numbers.

(a) 1005

(b) 1115

(c) 47

(d) 75

6.Find the squares of the following.

(a) \( 4\dfrac{1}{2} \)

(b) \( 7\dfrac{1}{2} \)

(c) \( 9\dfrac{1}{2} \)

(d) \( 11\dfrac{1}{2} \)

7.Show that 900 is a perfect square.

8.Show that 5478 is not a perfect square.

9.Show that 5776 is a perfect square.

10.Show that 6560 is not a perfect square.

11.Find the Pythagorean triplets , if one of the numbers is :

(a) 10

(b) 12

(c) 18

(d) 22

12.Express each of the following perfect squares as the sum of consecutive numbers.

(a) 121

(b) 100

(c) 25

(d) 169

13.Which of the numbers are perfect squares ? (use factorization method)

(a) 189

(b) 289

(c) 216

(d)  225

(e) 925

(f1025

(g) 3547

(h) 5832

14.Which of the numbers are not perfect squares ?

(a) 327

(b) 456

(c) 625

(d) 576

(e) 841

(f) 528

(g) 441

(h) 963

 

EXERCISE (B)

 

1.Find the square root of the following.

(a) 676

(b) 1225

(c) 1600

(d) \( 5^2\times4^2 \)

(e) \( 10\times5^2\times2^2 \)

(f) 169

(g) 3025

(h) 69696

2.Find the square root by repeated subtraction method.

(a) 144

(b) 225

(c) 121

(d) 81

3.Find the square root of the following by prime factorization method.

(a) 576

(b) 1089

(c) 2209

(d) 12321

(e) 14884

(f) 54756

(g) 110889

(h) 1225

4.By what smallest number must the following numbers be multiplied in order to make them perfect squares.

(a) 188

(b) 147

(c) 116

(d) 2028

5.By what smallest number must the following be divided to get the perfect square ?

(a) 3645

(b) 2844

(c) 450

(d) 180

6.For a class picnic , children collected ₹ 3481.Each child gives as many repees as there were children.How many children were there and how much money did each contribute ?

7.A cinema hall has 1849 seats in the form of rows, each rows containing as many seats as there  are rows.How many seats are there in each row?

 

EXERCISE (C)

 

1.Find the square root of the following by long division method.

(a) 9604

(b) 18769

(c) 222784

(d) 8464

(e) 11.9025

(f) 125.44

(g)  7.29

(h) 0.0529

(i) \( 3\dfrac{22}{49} \)

(j) \( 21\dfrac{51}{169} \)

(k) \( 2\dfrac{14}{25} \)

(l) \( 76\dfrac{9}{16} \)

2.Find the value of the following.

(a) \( \sqrt{\dfrac{1225}{1681}} \)

(b) \( \sqrt{\dfrac{3136}{484}} \)

(c) \( \sqrt{\dfrac{361}{225}} \)

(d) \( \sqrt{\dfrac{1849}{2809}} \)

(e) \( \sqrt{\dfrac{2.25}{2.56}} \)

(f) \( \sqrt{\dfrac{24.01}{31.36}} \)

(g) \( \sqrt{\dfrac{50625}{13225}} \)

(h) \( \sqrt{\dfrac{0.0081}{0.0289}} \)

3.Find the value of the following up to three decimal places.

(a) \( \sqrt{627} \)

(b) \( \sqrt{0.1331} \)

(c) \( \sqrt{\dfrac{1}{7}} \)

(d) \( \sqrt{0.32} \)

(e) \( \sqrt{\dfrac{7}{9}} \)

(f) \( \sqrt{6} \)

(g) \( \sqrt{2.7} \)

(h) \( \sqrt{15} \)

(i) \( \sqrt{0.10} \)

(j) \( \sqrt{1\dfrac{3}{8}} \)

(k) \( \sqrt{4\dfrac{2}{5}} \)

(l) \( \sqrt{3\dfrac{4}{11}} \)

4.Find the least number which must be subtracted from 48897 to obtain a perfect square.Also,find the perfect square number and its square root.

5.Find the least number which must be added to 3026 to obtain a perfect square.Also,find the perfect square number and its square root.

6.Find the greatest number of five digits which is a perfect square.Also,find its square root .

7.Find the length of each side of a square whose area is equal to the area of a rectangle of length 13.6 m and breadth is 3.4 m.

8.Find the least number which must be subtracted from 8157 to obtain a perfect square .Find the square number and its square root.

9.Find the decimal number which when multiplied by itself gives 53.8956 as the product.

10.Find the value of :

(a) \( \sqrt{64}+\sqrt{441} \)

(b) \( \dfrac{\sqrt{81}-\sqrt{25}}{\sqrt{81}+\sqrt{25}} \)

(c) \( \sqrt{28-\sqrt{576}} \)

(d) \( \sqrt{2601}+\sqrt{2.25} \)

11.Simplify:

\( \dfrac{\sqrt{77.44}+\sqrt{19.36}}{\sqrt{77.44}-\sqrt{19.36}} \)

12.Find the value of ​\( \sqrt{116281} \)​ and evaluate ​\( \sqrt{1162.81}+\sqrt{11.6281} \)

13.Find the value of \( \sqrt{0.0484} \)​and evaluate \( \sqrt{484}-\sqrt{0.000484} \)

14.What least number must be subtracted from 16160 to get a perfect square.Also,find the square root of the perfect square number so obtained.

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