Simplify square root of 45x- square root of 20x

$\sqrt{45 x} - \sqrt{20 x}$

Step 1

Simplify each term.

Rewrite $45 x$ as $3^{2} \cdot (5 x)$ .

Factor $9$ out of $45$ .

$\sqrt{9 (5) x} - \sqrt{20 x}$

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

$\sqrt{3^{2} \cdot 5 x} - \sqrt{20 x}$

Add parentheses.

$\sqrt{3^{2} \cdot (5 x)} - \sqrt{20 x}$

$\sqrt{3^{2} \cdot (5 x)} - \sqrt{20 x}$

Pull terms out from under the radical.

$3 \sqrt{5 x} - \sqrt{20 x}$

Rewrite $20 x$ as $2^{2} \cdot (5 x)$ .

Factor $4$ out of $20$ .

$3 \sqrt{5 x} - \sqrt{4 (5) x}$

Rewrite $4$ as $2^{2}$ .

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

Add parentheses.

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 1$ .

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

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

Step 2

Subtract $2 \sqrt{5 x}$ from $3 \sqrt{5 x}$ .

$\sqrt{5 x}$

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