Pre-Algebra Examples

$\sqrt{5 x^{2} \cdot \sqrt{15 x^{2}}}$

Step 1

Reorder $15$ and $x^{2}$ .

$\sqrt{5 x^{2} \sqrt{x^{2} \cdot 15}}$

Step 2

Pull terms out from under the radical.

$\sqrt{5 x^{2} x \sqrt{15}}$

Step 3

Combine exponents.

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Step 3.1

Raise $x$ to the power of $1$ .

$\sqrt{5 (x^{1} x^{2}) \sqrt{15}}$

Step 3.2

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

$\sqrt{5 x^{1 + 2} \sqrt{15}}$

Step 3.3

Add $1$ and $2$ .

$\sqrt{5 x^{3} \sqrt{15}}$

Step 4

Rewrite $5 x^{3} \sqrt{15}$ as $x^{2} \cdot (5 x \sqrt{15})$ .

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Step 4.1

Factor out $x^{2}$ .

$\sqrt{5 (x^{2} x) \sqrt{15}}$

Step 4.2

Reorder $5$ and $x^{2}$ .

$\sqrt{x^{2} \cdot 5 x \sqrt{15}}$

Step 4.3

Add parentheses.

$\sqrt{x^{2} \cdot 5 (x \sqrt{15})}$

Step 4.4

Add parentheses.

$\sqrt{x^{2} \cdot (5 x \sqrt{15})}$

Step 5

Pull terms out from under the radical.

$x \sqrt{5 x \sqrt{15}}$