Solve 23sqrt(7\div35) | Equatix

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Question

$$23 \sqrt{ 7 \div 35 }$$

$\frac{23\sqrt{5}}{5}\approx 10.285912696$

Reduce the fraction $\frac{7}{35}$ to lowest terms by extracting and canceling out $7$.

$$23\sqrt{\frac{1}{5}}$$

Rewrite the square root of the division $\sqrt{\frac{1}{5}}$ as the division of square roots $\frac{\sqrt{1}}{\sqrt{5}}$.

$$23\times \frac{\sqrt{1}}{\sqrt{5}}$$

Calculate the square root of $1$ and get $1$.

$$23\times \frac{1}{\sqrt{5}}$$

Rationalize the denominator of $\frac{1}{\sqrt{5}}$ by multiplying numerator and denominator by $\sqrt{5}$.

$$23\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of $\sqrt{5}$ is $5$.

$$23\times \frac{\sqrt{5}}{5}$$

Express $23\times \frac{\sqrt{5}}{5}$ as a single fraction.

$$\frac{23\sqrt{5}}{5}$$