Pre-Algebra Examples

$\sqrt{2 x^{5} \div 18}$

Step 1

Reduce the expression $2 x^{5} \div 18$ by cancelling the common factors.

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Step 1.1

Factor $2$ out of $2 x^{5}$ .

$\sqrt{2 (x^{5}) \div 18}$

Step 1.2

Factor $2$ out of $18$ .

$\sqrt{2 x^{5} \div 2 \cdot 9}$

Step 1.3

Cancel the common factor.

$\sqrt{2 x^{5} \div 2 \cdot 9}$

Step 1.4

Rewrite the expression.

$\sqrt{\frac{x^{5}}{9}}$

Step 2

Rewrite $\frac{x^{5}}{9}$ as ${(\frac{x^{2}}{3})}^{2} x$ .

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Step 2.1

Factor the perfect power ${(x^{2})}^{2}$ out of $x^{5}$ .

$\sqrt{\frac{{(x^{2})}^{2} x}{9}}$

Step 2.2

Factor the perfect power $3^{2}$ out of $9$ .

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

Step 2.3

Rearrange the fraction $\frac{{(x^{2})}^{2} x}{3^{2} \cdot 1}$ .

$\sqrt{{(\frac{x^{2}}{3})}^{2} x}$

Step 3

Pull terms out from under the radical.

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

Step 4

Combine $\frac{x^{2}}{3}$ and $\sqrt{x}$ .

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