Question

Which expression is equivalent to 4√6/3√2

Answer 1

Given

$\frac{4\sqrt{6}}{3\sqrt{2}} = \frac{4\sqrt{2\times3}}{3\sqrt{2}} \\ \\ = \frac{4\sqrt{2}\sqrt{3}}{3\sqrt{2}} = \frac{4}{3} \sqrt{3}$

Answer 2

Answer:

Step-by-step explanation:

The given expression is given as :

$\frac{4\sqrt{6}}{3\sqrt{2}}$

To solve the expression we rationalise the denominator as it is irrational by multiplying both numerator and denominator by $\sqrt{2}$

$\frac{4\sqrt{6}}{3\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}$

On multiplying the tems inside the roots we get

$\frac{4\sqrt{12}}{3\sqrt{4}}$

As factor of 12 are $=2\times2\times3$

On solving the square root we get

$\frac{8\sqrt{3}}{6}$

As both the numbers 8 and 6 are divisible by 2 on solving we get

$\frac{4\sqrt{3}}{3}$

is the final answer

Hope this will help