Algebra Examples

$x \sqrt{63 x^{2}} + 4 \sqrt{63 x^{4}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $63 x^{2}$ as ${(3 x)}^{2} \cdot 7$ .

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Step 1.1.1

Factor $9$ out of $63$ .

$x \sqrt{9 (7) x^{2}} + 4 \sqrt{63 x^{4}}$

Step 1.1.2

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

$x \sqrt{3^{2} \cdot 7 x^{2}} + 4 \sqrt{63 x^{4}}$

Step 1.1.3

Move $7$ .

$x \sqrt{3^{2} x^{2} \cdot 7} + 4 \sqrt{63 x^{4}}$

Step 1.1.4

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

$x \sqrt{{(3 x)}^{2} \cdot 7} + 4 \sqrt{63 x^{4}}$

Step 1.2

Pull terms out from under the radical.

$x (3 x \sqrt{7}) + 4 \sqrt{63 x^{4}}$

Step 1.3

Rewrite using the commutative property of multiplication.

$3 \sqrt{7} x \cdot x + 4 \sqrt{63 x^{4}}$

Step 1.4

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

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Step 1.4.1

Move $x$ .

$3 \sqrt{7} (x \cdot x) + 4 \sqrt{63 x^{4}}$

Step 1.4.2

Multiply $x$ by $x$ .

$3 \sqrt{7} x^{2} + 4 \sqrt{63 x^{4}}$

Step 1.5

Rewrite $63 x^{4}$ as ${(3 x^{2})}^{2} \cdot 7$ .

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Step 1.5.1

Factor $9$ out of $63$ .

$3 \sqrt{7} x^{2} + 4 \sqrt{9 (7) x^{4}}$

Step 1.5.2

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

$3 \sqrt{7} x^{2} + 4 \sqrt{3^{2} \cdot 7 x^{4}}$

Step 1.5.3

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

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

Step 1.5.4

Move $7$ .

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

Step 1.5.5

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

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

Step 1.6

Pull terms out from under the radical.

$3 \sqrt{7} x^{2} + 4 (3 x^{2} \sqrt{7})$

Step 1.7

Multiply $3$ by $4$ .

$3 \sqrt{7} x^{2} + 12 x^{2} \sqrt{7}$

Step 2

Simplify by adding terms.

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Step 2.1

Reorder the factors of $3 \sqrt{7} x^{2}$ .

$3 x^{2} \sqrt{7} + 12 x^{2} \sqrt{7}$

Step 2.2

Add $3 x^{2} \sqrt{7}$ and $12 x^{2} \sqrt{7}$ .

$15 x^{2} \sqrt{7}$