Finite Math Examples

$\sqrt{36 x^{3}} + \sqrt{25 x^{3}} - \sqrt{100 x^{3}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $36 x^{3}$ as ${(6 x)}^{2} x$ .

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Step 1.1.1

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} x^{3}} + \sqrt{25 x^{3}} - \sqrt{100 x^{3}}$

Step 1.1.2

Factor out $x^{2}$ .

$\sqrt{6^{2} (x^{2} x)} + \sqrt{25 x^{3}} - \sqrt{100 x^{3}}$

Step 1.1.3

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

$\sqrt{{(6 x)}^{2} x} + \sqrt{25 x^{3}} - \sqrt{100 x^{3}}$

Step 1.2

Pull terms out from under the radical.

$6 x \sqrt{x} + \sqrt{25 x^{3}} - \sqrt{100 x^{3}}$

Step 1.3

Rewrite $25 x^{3}$ as ${(5 x)}^{2} x$ .

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Step 1.3.1

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

$6 x \sqrt{x} + \sqrt{5^{2} x^{3}} - \sqrt{100 x^{3}}$

Step 1.3.2

Factor out $x^{2}$ .

$6 x \sqrt{x} + \sqrt{5^{2} (x^{2} x)} - \sqrt{100 x^{3}}$

Step 1.3.3

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

$6 x \sqrt{x} + \sqrt{{(5 x)}^{2} x} - \sqrt{100 x^{3}}$

Step 1.4

Pull terms out from under the radical.

$6 x \sqrt{x} + 5 x \sqrt{x} - \sqrt{100 x^{3}}$

Step 1.5

Rewrite $100 x^{3}$ as ${(10 x)}^{2} x$ .

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Step 1.5.1

Rewrite $100$ as $10^{2}$ .

$6 x \sqrt{x} + 5 x \sqrt{x} - \sqrt{10^{2} x^{3}}$

Step 1.5.2

Factor out $x^{2}$ .

$6 x \sqrt{x} + 5 x \sqrt{x} - \sqrt{10^{2} (x^{2} x)}$

Step 1.5.3

Rewrite $10^{2} x^{2}$ as ${(10 x)}^{2}$ .

$6 x \sqrt{x} + 5 x \sqrt{x} - \sqrt{{(10 x)}^{2} x}$

Step 1.6

Pull terms out from under the radical.

$6 x \sqrt{x} + 5 x \sqrt{x} - (10 x \sqrt{x})$

Step 1.7

Multiply $10$ by $- 1$ .

$6 x \sqrt{x} + 5 x \sqrt{x} - 10 x \sqrt{x}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $6 x \sqrt{x}$ and $5 x \sqrt{x}$ .

$11 x \sqrt{x} - 10 x \sqrt{x}$

Step 2.2

Subtract $10 x \sqrt{x}$ from $11 x \sqrt{x}$ .

$1 x \sqrt{x}$

Step 2.3

Multiply $x$ by $1$ .

$x \sqrt{x}$