Solve 156sqrt(157\div23) | Equatix

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Question

$$156 \sqrt{ 157 \div 23 }$$

$\frac{156\sqrt{3611}}{23}\approx 407.577786654$

Rewrite the square root of the division $\sqrt{\frac{157}{23}}$ as the division of square roots $\frac{\sqrt{157}}{\sqrt{23}}$.

$$156\times \frac{\sqrt{157}}{\sqrt{23}}$$

Rationalize the denominator of $\frac{\sqrt{157}}{\sqrt{23}}$ by multiplying numerator and denominator by $\sqrt{23}$.

$$156\times \frac{\sqrt{157}\sqrt{23}}{\left(\sqrt{23}\right)^{2}}$$

The square of $\sqrt{23}$ is $23$.

$$156\times \frac{\sqrt{157}\sqrt{23}}{23}$$

To multiply $\sqrt{157}$ and $\sqrt{23}$, multiply the numbers under the square root.

$$156\times \frac{\sqrt{3611}}{23}$$

Express $156\times \frac{\sqrt{3611}}{23}$ as a single fraction.

$$\frac{156\sqrt{3611}}{23}$$