Solve (4sqrt(6))\div(2sqrt(3)) | Equatix

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Question

$$(4 \sqrt{ 6 } ) \div (2 \sqrt{ 3 } )$$

$2\sqrt{2}\approx 2.828427125$

Cancel out $2$ in both numerator and denominator.

$$\frac{2\sqrt{6}}{\sqrt{3}}$$

Rationalize the denominator of $\frac{2\sqrt{6}}{\sqrt{3}}$ by multiplying numerator and denominator by $\sqrt{3}$.

$$\frac{2\sqrt{6}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

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

$$\frac{2\sqrt{6}\sqrt{3}}{3}$$

Factor $6=3\times 2$. Rewrite the square root of the product $\sqrt{3\times 2}$ as the product of square roots $\sqrt{3}\sqrt{2}$.

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

Multiply $\sqrt{3}$ and $\sqrt{3}$ to get $3$.

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

Cancel out $3$ and $3$.

$$2\sqrt{2}$$