Evaluate square root of 180-5 square root of 5+ square root of 20

$\sqrt{180} - 5 \sqrt{5} + \sqrt{20}$

Step 1

Simplify each term.

Rewrite $180$ as $6^{2} \cdot 5$ .

Factor $36$ out of $180$ .

$\sqrt{36 (5)} - 5 \sqrt{5} + \sqrt{20}$

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

$\sqrt{6^{2} \cdot 5} - 5 \sqrt{5} + \sqrt{20}$

$\sqrt{6^{2} \cdot 5} - 5 \sqrt{5} + \sqrt{20}$

Pull terms out from under the radical.

$6 \sqrt{5} - 5 \sqrt{5} + \sqrt{20}$

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

Factor $4$ out of $20$ .

$6 \sqrt{5} - 5 \sqrt{5} + \sqrt{4 (5)}$

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

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

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

Pull terms out from under the radical.

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

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

Step 2

Simplify by adding terms.

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

$\sqrt{5} + 2 \sqrt{5}$

Add $\sqrt{5}$ and $2 \sqrt{5}$ .

$3 \sqrt{5}$

$3 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{5}$

Decimal Form:

$6.70820393 \dots$

Related Questions