Question

What is the value of $\frac{16\sqrt{13}}{9\sqrt{52}}$ ?

• A. $\frac{3}{9}$
• B. $\frac{9}{8}$
• C. $\frac{7}{9}$
• D. $\frac{8}{9}$

Answer 1

The correct option is D

$\frac{8}{9}$

The prime factorisation of the number 52 is 13 $\times$ 2 $\times$ 2. $\sqrt{52}$ $=\sqrt{13\times 2\times 2}=2\sqrt{13}$
So, $9\sqrt{52}$ can be written as 9 $\times$ 2$\sqrt{13}$ = 18 $\sqrt{13}$
Basically we are diving $16\sqrt{13}÷9\sqrt{52}$ which is equilvalent to $16\sqrt{13}$ ÷ 18 $\sqrt{13}$
On division, we find that the answer in the form of $\frac{p}{q}$ which is $\frac{8}{9}$.