Solve 23sqrt(7\div3/5) | Equatix

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Question

$$23 \sqrt{ 7 \div 3/5 }$$

$\frac{23\sqrt{105}}{15}\approx 15.711991174$

Express $\frac{\frac{7}{3}}{5}$ as a single fraction.

$$23\sqrt{\frac{7}{3\times 5}}$$

Multiply $3$ and $5$ to get $15$.

$$23\sqrt{\frac{7}{15}}$$

Rewrite the square root of the division $\sqrt{\frac{7}{15}}$ as the division of square roots $\frac{\sqrt{7}}{\sqrt{15}}$.

$$23\times \frac{\sqrt{7}}{\sqrt{15}}$$

Rationalize the denominator of $\frac{\sqrt{7}}{\sqrt{15}}$ by multiplying numerator and denominator by $\sqrt{15}$.

$$23\times \frac{\sqrt{7}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of $\sqrt{15}$ is $15$.

$$23\times \frac{\sqrt{7}\sqrt{15}}{15}$$

To multiply $\sqrt{7}$ and $\sqrt{15}$, multiply the numbers under the square root.

$$23\times \frac{\sqrt{105}}{15}$$

Express $23\times \frac{\sqrt{105}}{15}$ as a single fraction.

$$\frac{23\sqrt{105}}{15}$$