Question

Simplify

$\frac{3}{4}\sqrt{\frac{28}{3}}$

Short answer

The final answer is $\frac{3}{4}\sqrt{\frac{28}{3}}=\frac{3}{2}\sqrt{\frac{7}{3}}.$

Step-by-step solution

Step 1. Given information:

The given expression is $\frac{3}{4}\sqrt{\frac{28}{3}}$ .

Step 2. Concept use.

Separate the factors into their own square roots.

Dividing by its denominator.

Step 3. Applying the concept.    

Write the factors of given fractions separately.

$\frac{3}{4}\sqrt{\frac{28}{3}}=\frac{3}{4}\sqrt{\frac{2^2\times 7}{3}}$

$=\frac{3}{4}\times 2\sqrt{\frac{7}{3}}$

$=\pm \frac{3}{2}\sqrt{\frac{7}{3}}$

Since square root is positive quantity so we neglect negative sign.

Therefore, the simplified form is $\frac{3}{4}\sqrt{\frac{28}{3}}=\frac{3}{2}\sqrt{\frac{7}{3}}.$