Simplify (4 square root of 15)/(2 square root of 6)

$\frac{4 \sqrt{15}}{2 \sqrt{6}}$

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 \sqrt{15}$ .

$\frac{2 (2 \sqrt{15})}{2 \sqrt{6}}$

Cancel the common factors.

Factor $2$ out of $2 \sqrt{6}$ .

$\frac{2 (2 \sqrt{15})}{2 (\sqrt{6})}$

Cancel the common factor.

$\frac{2 (2 \sqrt{15})}{2 \sqrt{6}}$

Rewrite the expression.

$\frac{2 \sqrt{15}}{\sqrt{6}}$

Combine $\sqrt{15}$ and $\sqrt{6}$ into a single radical.

$2 \sqrt{\frac{15}{6}}$

Cancel the common factor of $15$ and $6$ .

Factor $3$ out of $15$ .

$2 \sqrt{\frac{3 (5)}{6}}$

Cancel the common factors.

Factor $3$ out of $6$ .

$2 \sqrt{\frac{3 \cdot 5}{3 \cdot 2}}$

Cancel the common factor.

$2 \sqrt{\frac{3 \cdot 5}{3 \cdot 2}}$

Rewrite the expression.

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

Rewrite $\sqrt{\frac{5}{2}}$ as $\frac{\sqrt{5}}{\sqrt{2}}$ .

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

Multiply $\frac{\sqrt{5}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$2 (\frac{\sqrt{5}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}})$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{5}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Raise $\sqrt{2}$ to the power of $1$ .

$2 \frac{\sqrt{5} \sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}}$

Raise $\sqrt{2}$ to the power of $1$ .

$2 \frac{\sqrt{5} \sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 \frac{\sqrt{5} \sqrt{2}}{{\sqrt{2}}^{1 + 1}}$

Add $1$ and $1$ .

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

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$2 \frac{\sqrt{5} \sqrt{2}}{{(2^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 \frac{\sqrt{5} \sqrt{2}}{2^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$2 \frac{\sqrt{5} \sqrt{2}}{2^{1}}$

Evaluate the exponent.

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

Simplify the numerator.

Combine using the product rule for radicals.

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

Multiply $5$ by $2$ .

$2 \frac{\sqrt{10}}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{\sqrt{10}}{2}$

Rewrite the expression.

$\sqrt{10}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{10}$

Decimal Form:

$3.16227766 \dots$

Simplify (4 square root of 15)/(2 square root of 6)

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