Simplify square root of 72x- square root of 50x

$\sqrt{72 x} - \sqrt{50 x}$

Step 1

Simplify each term.

Rewrite $72 x$ as $6^{2} \cdot (2 x)$ .

Factor $36$ out of $72$ .

$\sqrt{36 (2) x} - \sqrt{50 x}$

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

$\sqrt{6^{2} \cdot 2 x} - \sqrt{50 x}$

Add parentheses.

$\sqrt{6^{2} \cdot (2 x)} - \sqrt{50 x}$

$\sqrt{6^{2} \cdot (2 x)} - \sqrt{50 x}$

Pull terms out from under the radical.

$6 \sqrt{2 x} - \sqrt{50 x}$

Rewrite $50 x$ as $5^{2} \cdot (2 x)$ .

Factor $25$ out of $50$ .

$6 \sqrt{2 x} - \sqrt{25 (2) x}$

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

$6 \sqrt{2 x} - \sqrt{5^{2} \cdot 2 x}$

Add parentheses.

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

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

Pull terms out from under the radical.

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

Multiply $5$ by $- 1$ .

$6 \sqrt{2 x} - 5 \sqrt{2 x}$

$6 \sqrt{2 x} - 5 \sqrt{2 x}$

Step 2

Subtract $5 \sqrt{2 x}$ from $6 \sqrt{2 x}$ .

$\sqrt{2 x}$

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