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

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Question

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

$\frac{23\sqrt{105}}{105}\approx 2.244570168$

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

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

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

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

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

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

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

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

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

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

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

$$23\times \frac{\frac{\sqrt{105}}{15}}{7}$$

Express $\frac{\frac{\sqrt{105}}{15}}{7}$ as a single fraction.

$$23\times \frac{\sqrt{105}}{15\times 7}$$

Multiply $15$ and $7$ to get $105$.

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

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

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