Evaluate (7 square root of 15)/( square root of 18)

$\frac{7 \sqrt{15}}{\sqrt{18}}$

Step 1

Combine $\sqrt{15}$ and $\sqrt{18}$ into a single radical.

$7 \sqrt{\frac{15}{18}}$

Step 2

Cancel the common factor of $15$ and $18$ .

Factor $3$ out of $15$ .

$7 \sqrt{\frac{3 (5)}{18}}$

Cancel the common factors.

Factor $3$ out of $18$ .

$7 \sqrt{\frac{3 \cdot 5}{3 \cdot 6}}$

Cancel the common factor.

$7 \sqrt{\frac{3 \cdot 5}{3 \cdot 6}}$

Rewrite the expression.

$7 \sqrt{\frac{5}{6}}$

Step 3

Rewrite $\sqrt{\frac{5}{6}}$ as $\frac{\sqrt{5}}{\sqrt{6}}$ .

$7 \frac{\sqrt{5}}{\sqrt{6}}$

Step 4

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

$7 (\frac{\sqrt{5}}{\sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}})$

Step 5

Combine and simplify the denominator.

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

$7 \frac{\sqrt{5} \sqrt{6}}{\sqrt{6} \sqrt{6}}$

Raise $\sqrt{6}$ to the power of $1$ .

$7 \frac{\sqrt{5} \sqrt{6}}{{\sqrt{6}}^{1} \sqrt{6}}$

Raise $\sqrt{6}$ to the power of $1$ .

$7 \frac{\sqrt{5} \sqrt{6}}{{\sqrt{6}}^{1} {\sqrt{6}}^{1}}$

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

$7 \frac{\sqrt{5} \sqrt{6}}{{\sqrt{6}}^{1 + 1}}$

Add $1$ and $1$ .

$7 \frac{\sqrt{5} \sqrt{6}}{{\sqrt{6}}^{2}}$

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$7 \frac{\sqrt{5} \sqrt{6}}{{(6^{\frac{1}{2}})}^{2}}$

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

$7 \frac{\sqrt{5} \sqrt{6}}{6^{\frac{1}{2} \cdot 2}}$

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

$7 \frac{\sqrt{5} \sqrt{6}}{6^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$7 \frac{\sqrt{5} \sqrt{6}}{6^{\frac{2}{2}}}$

Rewrite the expression.

$7 \frac{\sqrt{5} \sqrt{6}}{6^{1}}$

Evaluate the exponent.

$7 \frac{\sqrt{5} \sqrt{6}}{6}$

Step 6

Simplify the numerator.

Combine using the product rule for radicals.

$7 \frac{\sqrt{5 \cdot 6}}{6}$

Multiply $5$ by $6$ .

$7 \frac{\sqrt{30}}{6}$

Step 7

Combine $7$ and $\frac{\sqrt{30}}{6}$ .

$\frac{7 \sqrt{30}}{6}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{7 \sqrt{30}}{6}$

Decimal Form:

$6.39009650 \dots$

Evaluate (7 square root of 15)/( square root of 18)

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