Solve \frac { - 4 } { 3 } \sqrt { \frac { 3 } { 4 } }

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Question

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

$-\frac{2\sqrt{3}}{3}\approx -1.154700538$

Fraction $\frac{-4}{3}$ can be rewritten as $-\frac{4}{3}$ by extracting the negative sign.

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

Rewrite the square root of the division $\sqrt{\frac{3}{4}}$ as the division of square roots $\frac{\sqrt{3}}{\sqrt{4}}$.

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

Calculate the square root of $4$ and get $2$.

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

Multiply $-\frac{4}{3}$ times $\frac{\sqrt{3}}{2}$ by multiplying numerator times numerator and denominator times denominator.

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

Cancel out $2$ in both numerator and denominator.

$$\frac{-2\sqrt{3}}{3}$$