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Squares And Square Roots

Question
CBSEENMA8002476
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Find the square of the following numbers containing 5 in unit’s place.

(i) 15 (ii) 95 (iii) 105 (iv) 205

Solution

(i)    (15)2 = 1 x (1 + 1) x 100 + 25
                = 1 x 2 x 100 + 25
                = 200 + 25 = 225
(ii)    (95)2 = 9 x (9 + 1) x 100 + 25
                = 9 x 10 x 100 + 25
                = 9000 + 25 = 9025
(iii)   (105)2 = 10 x (10 + 1) x 100 + 25
                = 10 x 11 x 100 + 25
                = 11000 + 25 = 11025
(iv)    (205)2 = 20 x (20 + 1) x 100 + 25
                = 20 x 21 x 100 + 25
                = 42000 + 25 = 42025  

Some More Questions From Squares and Square Roots Chapter

The square of which of the following numbers would be an odd number/an even number?

Why?

(i) 727 (ii) 158 (iii) 269 (iv) 1980

What will be the number of zeros in the square of the following numbers?

(i) 60 (ii) 400

How many natural numbers lie between 92 and 102? Between 112 and 122?

How many non-square numbers lie between the following pairs of numbers:
(i) 1002 and 1012 (ii) 902 and 912
(iii) 10002 and 10012

Find whether each of the following numbers is a perfect square or not?

(i) 121 (ii) 55 (iii) 81

(iv) 49 (v) 69

Do you think the reverse is also true, i.e. is the sum of any two consecutive positive integers is perfect square of a number? Give example to support your answer.

The difference between the squares of two consecutive natural numbers is equal to the sum of the two numbers.

Write the square, making use of the above pattern.

(i) 1111112 (ii) 11111112

Can you find the square of the following numbers using the above pattern?

(i) 66666672 (ii) 666666672

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