Question

Fill in the blanks.
(i) 1 + 3 + 5 + 7 + 9 + 11 + 13 = (.........)².
(ii) $\sqrt{1681}=.........$
(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.

Answer 1

(i) $1+3+5+7+9+11+13=(7{)}^2$


(ii)

$\sqrt{1681}=41$

(iii) The smallest square number exactly divisible by 2, 4 and 6 is 36.

$$\begin{gathered} \mathrm{LCM}\mathrm{of}2,4\mathrm{and}6\mathrm{is}12. \\ \mathrm{Prime}\mathrm{factorisation}\mathrm{of}12=2\times 2\times 3 \\ \mathrm{To}\mathrm{make}\mathrm{it}\mathrm{a}\mathrm{perfect}\mathrm{square},\mathrm{we}\mathrm{need}\mathrm{to}\mathrm{multiply}\mathrm{it}\mathrm{by}3. \\ \therefore 12\times 3=36 \end{gathered}$$

(iv) A given number is a perfect square having n digits, where n is odd. then, its square root will have $\left(\frac{n+1}{2}\right)$ digits.