Blackberry publications class 8 maths Square and Square roots

SQUARES AND SQUARE ROOTS

 

EXERCISE 7(A)

 

1.Write the unit’s digits 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 numbers ?
(a)64
(b)441
(c)792
(d)252

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 a perfect square.
9.Show that 5776 is a perfect square.
10.Show that 6560 is a perfect square.

11.Find the phythagorean triplets, one of whose numbers is:
(a)10
(b)12
(c)18
(d)22
(e)30

12.Express each of the following perfect squares as the sum of similar numbers:
(a)121
(b)100
(c)25
(d)169
(e)225

13.Which of the numbers are perfect squares? (use factorization method)
(a)189
(b)289
(c)216
(d)225
(e)925
(f)1025
(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 7(B)

1.Find the square root of the following:
(a)676
(b)1225
(c)1600
(d)​\( 5^2\times{4^3} \)
(e)​\( 10\times{5^3}\times{2^3} \)
(f)169
(g)3025
(h)69696

2.Find the square root by the method of repeated subtraction:
(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 be 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 give as many rupees as there where children.How many children were there and how much money did each contribute ?

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

8.What least number must be subtracted from 16160 to get a perfect square ? Also, find the square root of this perfect square.

EXERCISE 7(C)

1.Find the square root of :
(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 :
(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 upto 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 and its square root.

5.Find the least number which must be added to 3026 to obtain a perfect square.Also,find this perfect square 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 meters and breadth 3.4 meters.

8.Find the least number which must be subtracted from 8157 to obtain a perfect square.Also,find the perfect square 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)​\( \sqrt{26.01}+\sqrt{2.25} \)

11.Simplify:​\( \dfrac{\sqrt{77.44}+\sqrt{19.36}}{\sqrt{77.44}-\sqrt{19.36}} \)

12.Find the value of ​\( \sqrt{116281} \)​ and calculate ​\( \sqrt{116.281}+\sqrt{11.6281} \)

13.Find ​\( \sqrt{0.484} \)​ and calculate ​\( \sqrt{484}-\sqrt{0.000484} \)

14.Find the perimeter, if a square whose area is 196 ​\( m^2 \)​.

15.Find the length of each side of a square field, if the area of the field is ​\( 40\dfrac{2865}{529}m^2 \)​.

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