Evaluate 7 square root of 5-2 square root of 20

$7 \sqrt{5} - 2 \sqrt{20}$

Step 1

Simplify each term.

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

Factor $4$ out of $20$ .

$7 \sqrt{5} - 2 \sqrt{4 (5)}$

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

$7 \sqrt{5} - 2 \sqrt{2^{2} \cdot 5}$

$7 \sqrt{5} - 2 \sqrt{2^{2} \cdot 5}$

Pull terms out from under the radical.

$7 \sqrt{5} - 2 (2 \sqrt{5})$

Multiply $2$ by $- 2$ .

$7 \sqrt{5} - 4 \sqrt{5}$

$7 \sqrt{5} - 4 \sqrt{5}$

Step 2

Subtract $4 \sqrt{5}$ from $7 \sqrt{5}$ .

$3 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{5}$

Decimal Form:

$6.70820393 \dots$

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