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Squares And Square Roots

Question

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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.

Solution

Any natural number ending in 0, 1, 4, 5, 6 or 9 can be or cannot be a square-number. Five such numbers are:

56790, 3671, 2454, 76555, 69209

Property 2. If a number has 1 or 9 in the unit’s place, then its square ends in 1.

For example:

(1)² = 1, (9)² = 81, (11)² = 121, (19)² = 361, (21)² = 441.

Some More Questions From Squares and Square Roots Chapter

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

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

(i) 121 (ii) 55 (iii) 81

(iv) 49 (v) 69

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