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Squares And Square Roots

Question

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Express 19² as the sum of two consecutive integers.

Solution

(i) 52 (ii) 62

Some More Questions From Squares and Square Roots Chapter

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

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.

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