Algebra Examples

$x \sqrt{6 x^{2}} + 3 \sqrt{150 x^{4}}$

Step 1

Simplify each term.

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Step 1.1

Reorder $6$ and $x^{2}$ .

$x \sqrt{x^{2} \cdot 6} + 3 \sqrt{150 x^{4}}$

Step 1.2

Pull terms out from under the radical.

$x (x \sqrt{6}) + 3 \sqrt{150 x^{4}}$

Step 1.3

Rewrite using the commutative property of multiplication.

$\sqrt{6} x \cdot x + 3 \sqrt{150 x^{4}}$

Step 1.4

Multiply $x$ by $x$ by adding the exponents.

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Step 1.4.1

Move $x$ .

$\sqrt{6} (x \cdot x) + 3 \sqrt{150 x^{4}}$

Step 1.4.2

Multiply $x$ by $x$ .

$\sqrt{6} x^{2} + 3 \sqrt{150 x^{4}}$

Step 1.5

Rewrite $150 x^{4}$ as ${(5 x^{2})}^{2} \cdot 6$ .

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Step 1.5.1

Factor $25$ out of $150$ .

$\sqrt{6} x^{2} + 3 \sqrt{25 (6) x^{4}}$

Step 1.5.2

Rewrite $25$ as $5^{2}$ .

$\sqrt{6} x^{2} + 3 \sqrt{5^{2} \cdot 6 x^{4}}$

Step 1.5.3

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$\sqrt{6} x^{2} + 3 \sqrt{5^{2} \cdot 6 {(x^{2})}^{2}}$

Step 1.5.4

Move $6$ .

$\sqrt{6} x^{2} + 3 \sqrt{5^{2} {(x^{2})}^{2} \cdot 6}$

Step 1.5.5

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

$\sqrt{6} x^{2} + 3 \sqrt{{(5 x^{2})}^{2} \cdot 6}$

Step 1.6

Pull terms out from under the radical.

$\sqrt{6} x^{2} + 3 (5 x^{2} \sqrt{6})$

Step 1.7

Multiply $5$ by $3$ .

$\sqrt{6} x^{2} + 15 x^{2} \sqrt{6}$

Step 2

Simplify by adding terms.

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Step 2.1

Reorder the factors of $\sqrt{6} x^{2}$ .

$x^{2} \sqrt{6} + 15 x^{2} \sqrt{6}$

Step 2.2

Add $x^{2} \sqrt{6}$ and $15 x^{2} \sqrt{6}$ .

$16 x^{2} \sqrt{6}$