Solve 4sqrt(4\div446) | Equatix

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Question

$$4 \sqrt{ 4 \div 446 }$$

$\frac{4\sqrt{446}}{223}\approx 0.378810979$

Reduce the fraction $\frac{4}{446}$ to lowest terms by extracting and canceling out $2$.

$$4\sqrt{\frac{2}{223}}$$

Rewrite the square root of the division $\sqrt{\frac{2}{223}}$ as the division of square roots $\frac{\sqrt{2}}{\sqrt{223}}$.

$$4\times \frac{\sqrt{2}}{\sqrt{223}}$$

Rationalize the denominator of $\frac{\sqrt{2}}{\sqrt{223}}$ by multiplying numerator and denominator by $\sqrt{223}$.

$$4\times \frac{\sqrt{2}\sqrt{223}}{\left(\sqrt{223}\right)^{2}}$$

The square of $\sqrt{223}$ is $223$.

$$4\times \frac{\sqrt{2}\sqrt{223}}{223}$$

To multiply $\sqrt{2}$ and $\sqrt{223}$, multiply the numbers under the square root.

$$4\times \frac{\sqrt{446}}{223}$$

Express $4\times \frac{\sqrt{446}}{223}$ as a single fraction.

$$\frac{4\sqrt{446}}{223}$$