Solve 15sqrt(15\div579) | Equatix

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Question

$$15 \sqrt{ 15 \div 579 }$$

$\frac{15\sqrt{965}}{193}\approx 2.414335425$

Reduce the fraction $\frac{15}{579}$ to lowest terms by extracting and canceling out $3$.

$$15\sqrt{\frac{5}{193}}$$

Rewrite the square root of the division $\sqrt{\frac{5}{193}}$ as the division of square roots $\frac{\sqrt{5}}{\sqrt{193}}$.

$$15\times \frac{\sqrt{5}}{\sqrt{193}}$$

Rationalize the denominator of $\frac{\sqrt{5}}{\sqrt{193}}$ by multiplying numerator and denominator by $\sqrt{193}$.

$$15\times \frac{\sqrt{5}\sqrt{193}}{\left(\sqrt{193}\right)^{2}}$$

The square of $\sqrt{193}$ is $193$.

$$15\times \frac{\sqrt{5}\sqrt{193}}{193}$$

To multiply $\sqrt{5}$ and $\sqrt{193}$, multiply the numbers under the square root.

$$15\times \frac{\sqrt{965}}{193}$$

Express $15\times \frac{\sqrt{965}}{193}$ as a single fraction.

$$\frac{15\sqrt{965}}{193}$$