Algebra Examples

$- x^{3} \sqrt{3} + x \sqrt{147 x^{4}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $147 x^{4}$ as ${(7 x^{2})}^{2} \cdot 3$ .

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Step 1.1.1

Factor $49$ out of $147$ .

$- x^{3} \sqrt{3} + x \sqrt{49 (3) x^{4}}$

Step 1.1.2

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

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

Step 1.1.3

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

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

Step 1.1.4

Move $3$ .

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

Step 1.1.5

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

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

Rewrite using the commutative property of multiplication.

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

Step 1.4

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 1.4.1

Move $x^{2}$ .

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

Step 1.4.2

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

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Step 1.4.2.1

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

$- x^{3} \sqrt{3} + 7 \sqrt{3} (x^{2} x^{1})$

Step 1.4.2.2

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

$- x^{3} \sqrt{3} + 7 \sqrt{3} x^{2 + 1}$

Step 1.4.3

Add $2$ and $1$ .

$- x^{3} \sqrt{3} + 7 \sqrt{3} x^{3}$

Step 2

Simplify by adding terms.

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Step 2.1

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

$- x^{3} \sqrt{3} + 7 x^{3} \sqrt{3}$

Step 2.2

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

$6 x^{3} \sqrt{3}$