Question

(i) Find the square root of 169
(ii) Find the value of $\sqrt{248+\sqrt{(51+\sqrt{169}}}$

Answer 1

(i) To find $\sqrt{169}$
Prime factorisation of 169 is:
$\sqrt{169}=\sqrt{13\times 13}$
$\sqrt{169}=13$

(ii) To find : Value of $\sqrt{248+\sqrt{(51+\sqrt{169}}}$
$\sqrt{248+\sqrt{(51+\sqrt{13\times 13}}}$
$\sqrt{248+\sqrt{(51+(13)}}$
$\sqrt{248+\sqrt{(51+(13)}}=\sqrt{248+\sqrt{64}}$
$\sqrt{248+8}=\sqrt{256}$\
$=16$