Simplify (15 square root of 6)/(3 square root of 5)

$\frac{15 \sqrt{6}}{3 \sqrt{5}}$

Step 1

Cancel the common factor of $15$ and $3$ .

Factor $3$ out of $15 \sqrt{6}$ .

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

Cancel the common factors.

Factor $3$ out of $3 \sqrt{5}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Multiply $\frac{5 \sqrt{6}}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{5 \sqrt{6}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

Step 3

Combine and simplify the denominator.

Multiply $\frac{5 \sqrt{6}}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

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

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{5 \sqrt{6} \sqrt{5}}{{\sqrt{5}}^{1} \sqrt{5}}$

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{5 \sqrt{6} \sqrt{5}}{{\sqrt{5}}^{1} {\sqrt{5}}^{1}}$

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

$\frac{5 \sqrt{6} \sqrt{5}}{{\sqrt{5}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{5 \sqrt{6} \sqrt{5}}{{\sqrt{5}}^{2}}$

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

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$\frac{5 \sqrt{6} \sqrt{5}}{{(5^{\frac{1}{2}})}^{2}}$

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

$\frac{5 \sqrt{6} \sqrt{5}}{5^{\frac{1}{2} \cdot 2}}$

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

$\frac{5 \sqrt{6} \sqrt{5}}{5^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5 \sqrt{6} \sqrt{5}}{5^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{5 \sqrt{6} \sqrt{5}}{5^{1}}$

Evaluate the exponent.

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

Step 4

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $\sqrt{6} \sqrt{5}$ by $1$ .

$\sqrt{6} \sqrt{5}$

Step 5

Combine using the product rule for radicals.

$\sqrt{6 \cdot 5}$

Step 6

Multiply $6$ by $5$ .

$\sqrt{30}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\sqrt{30}$

Decimal Form:

$5.47722557 \dots$

Simplify (15 square root of 6)/(3 square root of 5)

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