Simplify (4 square root of 14)/( square root of 12)

$\frac{4 \sqrt{14}}{\sqrt{12}}$

Combine $\sqrt{14}$ and $\sqrt{12}$ into a single radical.

$4 \sqrt{\frac{14}{12}}$

Cancel the common factor of $14$ and $12$ .

Factor $2$ out of $14$ .

$4 \sqrt{\frac{2 (7)}{12}}$

Cancel the common factors.

Factor $2$ out of $12$ .

$4 \sqrt{\frac{2 \cdot 7}{2 \cdot 6}}$

Cancel the common factor.

$4 \sqrt{\frac{2 \cdot 7}{2 \cdot 6}}$

Rewrite the expression.

$4 \sqrt{\frac{7}{6}}$

Rewrite $\sqrt{\frac{7}{6}}$ as $\frac{\sqrt{7}}{\sqrt{6}}$ .

$4 \frac{\sqrt{7}}{\sqrt{6}}$

Multiply $\frac{\sqrt{7}}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$4 (\frac{\sqrt{7}}{\sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}})$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{7}}{\sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$4 \frac{\sqrt{7} \sqrt{6}}{\sqrt{6} \sqrt{6}}$

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

$4 \frac{\sqrt{7} \sqrt{6}}{{\sqrt{6}}^{1} \sqrt{6}}$

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

$4 \frac{\sqrt{7} \sqrt{6}}{{\sqrt{6}}^{1} {\sqrt{6}}^{1}}$

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

$4 \frac{\sqrt{7} \sqrt{6}}{{\sqrt{6}}^{1 + 1}}$

Add $1$ and $1$ .

$4 \frac{\sqrt{7} \sqrt{6}}{{\sqrt{6}}^{2}}$

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

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

$4 \frac{\sqrt{7} \sqrt{6}}{{(6^{\frac{1}{2}})}^{2}}$

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

$4 \frac{\sqrt{7} \sqrt{6}}{6^{\frac{1}{2} \cdot 2}}$

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

$4 \frac{\sqrt{7} \sqrt{6}}{6^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 \frac{\sqrt{7} \sqrt{6}}{6^{\frac{2}{2}}}$

Rewrite the expression.

$4 \frac{\sqrt{7} \sqrt{6}}{6^{1}}$

Evaluate the exponent.

$4 \frac{\sqrt{7} \sqrt{6}}{6}$

Simplify the numerator.

Combine using the product rule for radicals.

$4 \frac{\sqrt{7 \cdot 6}}{6}$

Multiply $7$ by $6$ .

$4 \frac{\sqrt{42}}{6}$

Simplify terms.

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$2 (2) \frac{\sqrt{42}}{6}$

Factor $2$ out of $6$ .

$2 \cdot 2 \frac{\sqrt{42}}{2 \cdot 3}$

Cancel the common factor.

$2 \cdot 2 \frac{\sqrt{42}}{2 \cdot 3}$

Rewrite the expression.

$2 \frac{\sqrt{42}}{3}$

Combine $2$ and $\frac{\sqrt{42}}{3}$ .

$\frac{2 \sqrt{42}}{3}$

The result can be shown in multiple forms.

Exact Form:

$\frac{2 \sqrt{42}}{3}$

Decimal Form:

$4.32049379 \dots$

Simplify (4 square root of 14)/( square root of 12)

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