Fill in the blanks.

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)

$\sqrt{1681}=41$

(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.

 

 

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