How to solve sqrt(3/5/6 imes4)

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve sqrt(3/5/6\times4) | Equatix

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Question

$$\sqrt{ 3/5/6 \times 4 }$$

Evaluate

$\frac{\sqrt{10}}{5}\approx 0.632455532$

Solution Steps

Express $\frac{\frac{3}{5}}{6}$ as a single fraction.

$$\sqrt{\frac{3}{5\times 6}\times 4}$$

Multiply $5$ and $6$ to get $30$.

$$\sqrt{\frac{3}{30}\times 4}$$

Reduce the fraction $\frac{3}{30}$ to lowest terms by extracting and canceling out $3$.

$$\sqrt{\frac{1}{10}\times 4}$$

Multiply $\frac{1}{10}$ and $4$ to get $\frac{4}{10}$.

$$\sqrt{\frac{4}{10}}$$

Reduce the fraction $\frac{4}{10}$ to lowest terms by extracting and canceling out $2$.

$$\sqrt{\frac{2}{5}}$$

Rewrite the square root of the division $\sqrt{\frac{2}{5}}$ as the division of square roots $\frac{\sqrt{2}}{\sqrt{5}}$.

$$\frac{\sqrt{2}}{\sqrt{5}}$$

Rationalize the denominator of $\frac{\sqrt{2}}{\sqrt{5}}$ by multiplying numerator and denominator by $\sqrt{5}$.

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

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

$$\frac{\sqrt{2}\sqrt{5}}{5}$$

To multiply $\sqrt{2}$ and $\sqrt{5}$, multiply the numbers under the square root.

$$\frac{\sqrt{10}}{5}$$

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