# Square and Square root

## Exercise 3 (A)

1.Find the square of the following numbers :

(i) 15

(ii) 48

(iii) ​$$\dfrac{6}{7}$$

(iv) ​$$\dfrac{21}{25}$$

(v) ​$$6\dfrac{3}{8}$$

(vi) 0.9

(vii) 1.1

(viii) 0.018

2.Determine whether square of the following numbers will be even or odd.(Do not find the square)

(i) 529

(ii) 30976

(iii) 893025

(iv) 6990736

3.Just by looking at the following numbers, give reason why they are not perfect squares.

(i) 4893

(ii) 65000

(iii) 4422

(iv) 89138

(v) 150087

4.Using prime factorization method, find which of the following are perfect square numbers.

(i) 100

(ii) 284

(iii) 784

(iv) 1444

(v) 768

(vi) 4225

(vii) 3375

(viii) 15625

5.Using prime factorization method, find the square root of the following numbers.

(i) 256

(ii) 1936

(iii) 3364

(iv) 5625

(v) 7744

(vi) 12544

6.Find the square root of the following fractions.

(i) ​$$\dfrac{529}{1225}$$

(ii) $$\dfrac{1444}{3249}$$

(iii) $$1\dfrac{396}{9604}$$

(iv) 0.01

(v) 0.1764

(vi) 0.00003136

7.Simplyfy:

(i) ​$$\sqrt{10^2-{6^2}}$$

(ii) ​$$\Bigg(-\sqrt{\dfrac{9}{16}}\Bigg)\Bigg(\sqrt{\dfrac{64}{81}}\Bigg)$$

(iii) ​$$\sqrt{\dfrac{16}{36}-\dfrac{1}{4}}$$

8.Find the square root of 1024. Hence find the value of ​$$\sqrt{10.24} + \sqrt{0.1024}+\sqrt{10240000}$$​.

9.Find the smallest number by which each of the given number s ,ust be multiplied so that the product is a perfect square. Also find the square root of this new number.

(i) 175

(ii) 325

(iii) 720

(iv) 3150

10.Find the smallest number by which each of the given numbers must be divided so that the quotient is a perfect square.Also find the square root of this quotient.

(i) 2700

(ii) 5488

(iii) 7203

(iv) 20886

11.Find the smallest number which is completely divisible by each of the numbers 10 , 16 and 24.

12.The children of class VIII of a school contributed ₹ 3025 for the Prime Minister’s National Relief Fund, contributing as much money as there are children in the class.How many children are there in the class ?

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