Question

$\frac{\sqrt{3} }{5} + \frac{2}{\sqrt{3} } = a\sqrt{3}$, where a is a fraction.
Find the value of a.

Answer 1

Given:

$\frac{\sqrt{3} }{5} +\frac{2}{\sqrt{3} } =a\sqrt{3}$

To find:

the value of a where a is a fraction

Solution:

simplify

$\frac{\sqrt{3} }{5} +\frac{2}{\sqrt{3} } =a\sqrt{3}$

take LCM and we get

$\frac{3+10}{\sqrt{3} } =a\sqrt{3}$

make a cross multiplication

⇒13=a×5×√3×√3

⇒13=a×5×3

⇒13=15a

⇒a=$\frac{13}{15}$

Hence, a=$\frac{13}{15}$