Question:
Fill in the blanks.
(i) 1 + 3 + 5 + 7 + 9 + 11 + 13 = (.........)2.
(ii) $\sqrt{1681}=\ldots \ldots \ldots$
(iii) The smallest square number exactly divisible by 2, 4, 6 is .........
(iv) A given number is a perfect square having n digits, where n is odd. Then, its square root will have ......... digits.
Solution:
(i) $1+3+5+7+9+11+13=(7)^{2}$
(ii).png)
$\sqrt{1681}=41$
(iii) The smallest square number exactly divisible by 2, 4 and 6 is 36.
LCM of 2,4 and 6 is 12 .
Prime factorisation of $12=2 \times 2 \times 3$
To make it a perfect square, we need to multiply it by 3 .
$\therefore 12 \times 3=36$
(iv) A given number is a perfect square having $\mathrm{n}$ digits, where $\mathrm{n}$ is odd. then, its square root will have $\left(\frac{n+1}{2}\right)$ digits.