How to solve sqrt(4/5/6 imes5)

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(4/5/6\times5) | Equatix

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Question

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

Evaluate

$\frac{\sqrt{6}}{3}\approx 0.816496581$

Solution Steps

Express $\frac{\frac{4}{5}}{6}$ as a single fraction.

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

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

$$\sqrt{\frac{4}{30}\times 5}$$

Reduce the fraction $\frac{4}{30}$ to lowest terms by extracting and canceling out $2$.

$$\sqrt{\frac{2}{15}\times 5}$$

Express $\frac{2}{15}\times 5$ as a single fraction.

$$\sqrt{\frac{2\times 5}{15}}$$

Multiply $2$ and $5$ to get $10$.

$$\sqrt{\frac{10}{15}}$$

Reduce the fraction $\frac{10}{15}$ to lowest terms by extracting and canceling out $5$.

$$\sqrt{\frac{2}{3}}$$

Rewrite the square root of the division $\sqrt{\frac{2}{3}}$ as the division of square roots $\frac{\sqrt{2}}{\sqrt{3}}$.

$$\frac{\sqrt{2}}{\sqrt{3}}$$

Rationalize the denominator of $\frac{\sqrt{2}}{\sqrt{3}}$ by multiplying numerator and denominator by $\sqrt{3}$.

$$\frac{\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of $\sqrt{3}$ is $3$.

$$\frac{\sqrt{2}\sqrt{3}}{3}$$

To multiply $\sqrt{2}$ and $\sqrt{3}$, multiply the numbers under the square root.

$$\frac{\sqrt{6}}{3}$$

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