Simplify (2a^2)/( square root of 12a^10)

$\frac{2 a^{2}}{\sqrt{12 a^{10}}}$

Simplify the denominator.

Rewrite $12 a^{10}$ as ${(2 a^{5})}^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$\frac{2 a^{2}}{\sqrt{4 (3) a^{10}}}$

Rewrite $4$ as $2^{2}$ .

$\frac{2 a^{2}}{\sqrt{2^{2} \cdot 3 a^{10}}}$

Rewrite $a^{10}$ as ${(a^{5})}^{2}$ .

$\frac{2 a^{2}}{\sqrt{2^{2} \cdot 3 {(a^{5})}^{2}}}$

Move $3$ .

$\frac{2 a^{2}}{\sqrt{2^{2} {(a^{5})}^{2} \cdot 3}}$

Rewrite $2^{2} {(a^{5})}^{2}$ as ${(2 a^{5})}^{2}$ .

$\frac{2 a^{2}}{\sqrt{{(2 a^{5})}^{2} \cdot 3}}$

Pull terms out from under the radical.

$\frac{2 a^{2}}{2 a^{5} \sqrt{3}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 a^{2}}{2 a^{5} \sqrt{3}}$

Rewrite the expression.

$\frac{a^{2}}{a^{5} \sqrt{3}}$

Cancel the common factor of $a^{2}$ and $a^{5}$ .

Multiply by $1$ .

$\frac{a^{2} \cdot 1}{a^{5} \sqrt{3}}$

Cancel the common factors.

Factor $a^{2}$ out of $a^{5} \sqrt{3}$ .

$\frac{a^{2} \cdot 1}{a^{2} (a^{3} \sqrt{3})}$

Cancel the common factor.

$\frac{a^{2} \cdot 1}{a^{2} (a^{3} \sqrt{3})}$

Rewrite the expression.

$\frac{1}{a^{3} \sqrt{3}}$

Multiply $\frac{1}{a^{3} \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{1}{a^{3} \sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

Combine and simplify the denominator.

Multiply $\frac{1}{a^{3} \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{\sqrt{3}}{a^{3} \sqrt{3} \sqrt{3}}$

Move $\sqrt{3}$ .

$\frac{\sqrt{3}}{a^{3} (\sqrt{3} \sqrt{3})}$

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{\sqrt{3}}{a^{3} ({\sqrt{3}}^{1} \sqrt{3})}$

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{\sqrt{3}}{a^{3} ({\sqrt{3}}^{1} {\sqrt{3}}^{1})}$

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

$\frac{\sqrt{3}}{a^{3} {\sqrt{3}}^{1 + 1}}$

Add $1$ and $1$ .

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

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{\sqrt{3}}{a^{3} {(3^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{3}}{a^{3} \cdot 3^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{3}}{a^{3} \cdot 3^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{3}}{a^{3} \cdot 3^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{3}}{a^{3} \cdot 3^{1}}$

Evaluate the exponent.

$\frac{\sqrt{3}}{a^{3} \cdot 3}$

Move $3$ to the left of $a^{3}$ .

$\frac{\sqrt{3}}{3 a^{3}}$

Simplify (2a^2)/( square root of 12a^10)

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