Algebra Examples

$\sqrt{75 x} - \sqrt{27 x}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $25$ out of $75$ .

$\sqrt{25 (3) x} - \sqrt{27 x}$

Step 1.1.2

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

$\sqrt{5^{2} \cdot 3 x} - \sqrt{27 x}$

Step 1.1.3

Add parentheses.

$\sqrt{5^{2} \cdot (3 x)} - \sqrt{27 x}$

$\sqrt{5^{2} \cdot (3 x)} - \sqrt{27 x}$

Step 1.2

Pull terms out from under the radical.

$5 \sqrt{3 x} - \sqrt{27 x}$

Step 1.3

Rewrite $27 x$ as $3^{2} \cdot (3 x)$ .

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Step 1.3.1

Factor $9$ out of $27$ .

$5 \sqrt{3 x} - \sqrt{9 (3) x}$

Step 1.3.2

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

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

Step 1.3.3

Add parentheses.

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

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

Step 1.4

Pull terms out from under the radical.

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

Step 1.5

Multiply $3$ by $- 1$ .

$5 \sqrt{3 x} - 3 \sqrt{3 x}$

$5 \sqrt{3 x} - 3 \sqrt{3 x}$

Step 2

Subtract $3 \sqrt{3 x}$ from $5 \sqrt{3 x}$ .

$2 \sqrt{3 x}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$