Algebra Examples

$\sqrt{75 x^{7}} \sqrt{75 x^{7}}$

Step 1

Rewrite $75 x^{7}$ as ${(5 x^{3})}^{2} \cdot (3 x)$ .

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Step 1.1

Factor $25$ out of $75$ .

$\sqrt{25 (3) x^{7}} \sqrt{75 x^{7}}$

Step 1.2

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

$\sqrt{5^{2} \cdot 3 x^{7}} \sqrt{75 x^{7}}$

Step 1.3

Factor out $x^{6}$ .

$\sqrt{5^{2} \cdot 3 (x^{6} x)} \sqrt{75 x^{7}}$

Step 1.4

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$\sqrt{5^{2} \cdot 3 ({(x^{3})}^{2} x)} \sqrt{75 x^{7}}$

Step 1.5

Move $3$ .

$\sqrt{5^{2} {(x^{3})}^{2} \cdot 3 x} \sqrt{75 x^{7}}$

Step 1.6

Rewrite $5^{2} {(x^{3})}^{2}$ as ${(5 x^{3})}^{2}$ .

$\sqrt{{(5 x^{3})}^{2} \cdot 3 x} \sqrt{75 x^{7}}$

Step 1.7

Add parentheses.

$\sqrt{{(5 x^{3})}^{2} \cdot (3 x)} \sqrt{75 x^{7}}$

Step 2

Pull terms out from under the radical.

$5 x^{3} \sqrt{3 x} \sqrt{75 x^{7}}$

Step 3

Rewrite $75 x^{7}$ as ${(5 x^{3})}^{2} \cdot (3 x)$ .

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Step 3.1

Factor $25$ out of $75$ .

$5 x^{3} \sqrt{3 x} \sqrt{25 (3) x^{7}}$

Step 3.2

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

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

Step 3.3

Factor out $x^{6}$ .

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

Step 3.4

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

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

Step 3.5

Move $3$ .

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

Step 3.6

Rewrite $5^{2} {(x^{3})}^{2}$ as ${(5 x^{3})}^{2}$ .

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

Step 3.7

Add parentheses.

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

Step 4

Pull terms out from under the radical.

$5 x^{3} \sqrt{3 x} (5 x^{3} \sqrt{3 x})$

Step 5

Multiply $x^{3}$ by $x^{3}$ by adding the exponents.

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Step 5.1

Move $x^{3}$ .

$5 (x^{3} x^{3}) \sqrt{3 x} (5 \sqrt{3 x})$

Step 5.2

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

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

Step 5.3

Add $3$ and $3$ .

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

Step 6

Multiply $5 x^{6} \sqrt{3 x} (5 \sqrt{3 x})$ .

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Step 6.1

Multiply $5$ by $5$ .

$25 x^{6} \sqrt{3 x} \sqrt{3 x}$

Step 6.2

Raise $\sqrt{3 x}$ to the power of $1$ .

$25 x^{6} ({\sqrt{3 x}}^{1} \sqrt{3 x})$

Step 6.3

Raise $\sqrt{3 x}$ to the power of $1$ .

$25 x^{6} ({\sqrt{3 x}}^{1} {\sqrt{3 x}}^{1})$

Step 6.4

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

$25 x^{6} {\sqrt{3 x}}^{1 + 1}$

Step 6.5

Add $1$ and $1$ .

$25 x^{6} {\sqrt{3 x}}^{2}$

Step 7

Rewrite ${\sqrt{3 x}}^{2}$ as $3 x$ .

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Step 7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x}$ as ${(3 x)}^{\frac{1}{2}}$ .

$25 x^{6} {({(3 x)}^{\frac{1}{2}})}^{2}$

Step 7.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$25 x^{6} {(3 x)}^{\frac{1}{2} \cdot 2}$

Step 7.3

Combine $\frac{1}{2}$ and $2$ .

$25 x^{6} {(3 x)}^{\frac{2}{2}}$

Step 7.4

Cancel the common factor of $2$ .

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Step 7.4.1

Cancel the common factor.

$25 x^{6} {(3 x)}^{\frac{2}{2}}$

Step 7.4.2

Rewrite the expression.

$25 x^{6} {(3 x)}^{1}$

Step 7.5

Simplify.

$25 x^{6} (3 x)$

Step 8

Rewrite using the commutative property of multiplication.

$25 \cdot 3 x^{6} x$

Step 9

Multiply $x^{6}$ by $x$ by adding the exponents.

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Step 9.1

Move $x$ .

$25 \cdot 3 (x \cdot x^{6})$

Step 9.2

Multiply $x$ by $x^{6}$ .

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Step 9.2.1

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

$25 \cdot 3 (x^{1} x^{6})$

Step 9.2.2

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

$25 \cdot 3 x^{1 + 6}$

Step 9.3

Add $1$ and $6$ .

$25 \cdot 3 x^{7}$

Step 10

Multiply $25$ by $3$ .

$75 x^{7}$