Question

Explain the properties of perfect squares along with examples.... no copy paste

Answer 1

Answer:

example for prefect square is √16,√4....

Answer 2

$\large\underline{\bigstar \: \: {\sf {Properties \ of \ perfect \ squares:-}}}$

1. The square of an even number is always an even number.

Examples :-

(i) 2 is even and 2² = 4, which is even.

(ii) 4 is even and 4² = 16, which is even.

2. The square of an odd number is always an odd number.

Examples :-

(i) 3 is odd and 3² = 9, which is odd.

(ii) 5 is odd and 5² = 25, which is odd.

3. The square of a proper fraction is a proper fraction less than the given fraction.

Examples :-

$\rm {(i)\ \frac{1}{2} \ is\ a\ proper\ fraction \ and \ \frac{1}{2}^{2}=\frac{1}{4} <\frac{1}{2} }\\\\\\\rm {(ii)\ \frac{2}{3} \ is\ a\ proper\ fraction \ and \ \frac{2}{3}^{2}=\frac{4}{9} <\frac{2}{3} }$

4. The square of a decimal fraction less than 1 is a smaller than the given decimal.

Examples :-

(i) 0.1 < 1 and (0.1)² = 0.01 < 0.1

(ii) 0.3 < 1 and (0.3)² = 0.9 < 0.3

5. A number ending in 2, 3, 7 or 8 is never a perfect square.

Examples :-

The numbers 72, 243 and 1098 end in 2, 3 and 8 respectively.

None of them is a perfect square.

6. A number ending in an odd number of zeroes is never a perfect square.

Examples :-

The numbers 690, 87000 and 4900000 end in one, three and five zeroes respectively.

None of them is a perfect square.