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Squares And Square Roots

Question
CBSEENMA8002500
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(–1) = 1. Is –1, a square root of 1?

(–2)2 = 4. Is –2, a square root of 4?

(–9)2 = 81. Is –9, a square root of 81?

Solution

(i) Since (–1) × (–1) = 1

i.e. (–1)2 = 1

 ∴ Square root of 1 can also be –1.

Similarly,

(ii) Yes (–2) is a square root of 4.

(iii) Yes (–9) is a square root of 81.
Since we have to consider the positive square roots only and the symbol for a  positive square root is square root of blank end root.

∴  space space space space space space space square root of 16 = 4 (and not (-4)

    Similarly,   space space space square root of 25  means, the positive square root of 25 i.e. 5.
We can also find the square root by subtracting successive odd numbers starting from 1.

Some More Questions From Squares and Square Roots Chapter

Find the perfect square numbers between (i) 30 and 40 and (ii) 50 and 60.

1. Can we say whether the following numbers are perfect squares? How do we know?

(i) 1057 (ii) 23453 (iii) 7928

(iv) 222222 (v) 1069 (vi) 2061

Write five numbers which you can decide by looking at their one’s digit that they are not square numbers.

Write five numbers which you cannot decide just by looking at their unit’s digit (or one’s place) whether they are square numbers or not.

Which of 1232, 772 822, 1612, 1092 would end with digit 1?

Which of the following numbers would have digit 6 at unit place.

(i) 192 (ii) 242 (iii) 262

(iv) 362 (v) 342

What will be the “one’s digit” in the square of the following numbers?

(i) 1234 (ii) 26387 (iii) 52698

(iv) 99880 (v) 21222 (vi) 9106

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

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