Evaluate square root of 14-3 square root of 20

$\sqrt{14 - 3 \sqrt{20}}$

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

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Factor $4$ out of $20$ .

$\sqrt{14 - 3 \sqrt{4 (5)}}$

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

$\sqrt{14 - 3 \sqrt{2^{2} \cdot 5}}$

Pull terms out from under the radical.

$\sqrt{14 - 3 (2 \sqrt{5})}$

Multiply $2$ by $- 3$ .

$\sqrt{14 - 6 \sqrt{5}}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{14 - 6 \sqrt{5}}$

Decimal Form:

$0.76393202 \dots$

Evaluate square root of 14-3 square root of 20

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