Pre-Algebra Examples

$\sqrt{98 x^{5}} - 2 x \sqrt{18 x^{3}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $98 x^{5}$ as ${(7 x^{2})}^{2} \cdot (2 x)$ .

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Step 1.1.1

Factor $49$ out of $98$ .

$\sqrt{49 (2) x^{5}} - 2 x \sqrt{18 x^{3}}$

Step 1.1.2

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2} \cdot 2 x^{5}} - 2 x \sqrt{18 x^{3}}$

Step 1.1.3

Factor out $x^{4}$ .

$\sqrt{7^{2} \cdot 2 (x^{4} x)} - 2 x \sqrt{18 x^{3}}$

Step 1.1.4

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

$\sqrt{7^{2} \cdot 2 ({(x^{2})}^{2} x)} - 2 x \sqrt{18 x^{3}}$

Step 1.1.5

Move $2$ .

$\sqrt{7^{2} {(x^{2})}^{2} \cdot 2 x} - 2 x \sqrt{18 x^{3}}$

Step 1.1.6

Rewrite $7^{2} {(x^{2})}^{2}$ as ${(7 x^{2})}^{2}$ .

$\sqrt{{(7 x^{2})}^{2} \cdot 2 x} - 2 x \sqrt{18 x^{3}}$

Step 1.1.7

Add parentheses.

$\sqrt{{(7 x^{2})}^{2} \cdot (2 x)} - 2 x \sqrt{18 x^{3}}$

Step 1.2

Pull terms out from under the radical.

$7 x^{2} \sqrt{2 x} - 2 x \sqrt{18 x^{3}}$

Step 1.3

Rewrite $18 x^{3}$ as ${(3 x)}^{2} \cdot (2 x)$ .

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Step 1.3.1

Factor $9$ out of $18$ .

$7 x^{2} \sqrt{2 x} - 2 x \sqrt{9 (2) x^{3}}$

Step 1.3.2

Rewrite $9$ as $3^{2}$ .

$7 x^{2} \sqrt{2 x} - 2 x \sqrt{3^{2} \cdot 2 x^{3}}$

Step 1.3.3

Factor out $x^{2}$ .

$7 x^{2} \sqrt{2 x} - 2 x \sqrt{3^{2} \cdot 2 (x^{2} x)}$

Step 1.3.4

Move $2$ .

$7 x^{2} \sqrt{2 x} - 2 x \sqrt{3^{2} x^{2} \cdot 2 x}$

Step 1.3.5

Rewrite $3^{2} x^{2}$ as ${(3 x)}^{2}$ .

$7 x^{2} \sqrt{2 x} - 2 x \sqrt{{(3 x)}^{2} \cdot 2 x}$

Step 1.3.6

Add parentheses.

$7 x^{2} \sqrt{2 x} - 2 x \sqrt{{(3 x)}^{2} \cdot (2 x)}$

Step 1.4

Pull terms out from under the radical.

$7 x^{2} \sqrt{2 x} - 2 x (3 x \sqrt{2 x})$

Step 1.5

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

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Step 1.5.1

Move $x$ .

$7 x^{2} \sqrt{2 x} - 2 (x \cdot x) (3 \sqrt{2 x})$

Step 1.5.2

Multiply $x$ by $x$ .

$7 x^{2} \sqrt{2 x} - 2 x^{2} (3 \sqrt{2 x})$

Step 1.6

Multiply $3$ by $- 2$ .

$7 x^{2} \sqrt{2 x} - 6 x^{2} \sqrt{2 x}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $6 x^{2} \sqrt{2 x}$ from $7 x^{2} \sqrt{2 x}$ .

$1 x^{2} \sqrt{2 x}$

Step 2.2

Multiply $x^{2}$ by $1$ .

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