__SQUARES 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 \( 40\dfrac{2865}{529}m^2 \).**