Simplify square root of 80- square root of 45+3 square root of 2

$\sqrt{80} - \sqrt{45} + 3 \sqrt{2}$

Step 1

Simplify each term.

Rewrite $80$ as $4^{2} \cdot 5$ .

Factor $16$ out of $80$ .

$\sqrt{16 (5)} - \sqrt{45} + 3 \sqrt{2}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 5} - \sqrt{45} + 3 \sqrt{2}$

$\sqrt{4^{2} \cdot 5} - \sqrt{45} + 3 \sqrt{2}$

Pull terms out from under the radical.

$4 \sqrt{5} - \sqrt{45} + 3 \sqrt{2}$

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

Factor $9$ out of $45$ .

$4 \sqrt{5} - \sqrt{9 (5)} + 3 \sqrt{2}$

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

$4 \sqrt{5} - \sqrt{3^{2} \cdot 5} + 3 \sqrt{2}$

$4 \sqrt{5} - \sqrt{3^{2} \cdot 5} + 3 \sqrt{2}$

Pull terms out from under the radical.

$4 \sqrt{5} - (3 \sqrt{5}) + 3 \sqrt{2}$

Multiply $3$ by $- 1$ .

$4 \sqrt{5} - 3 \sqrt{5} + 3 \sqrt{2}$

$4 \sqrt{5} - 3 \sqrt{5} + 3 \sqrt{2}$

Step 2

Subtract $3 \sqrt{5}$ from $4 \sqrt{5}$ .

$\sqrt{5} + 3 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{5} + 3 \sqrt{2}$

Decimal Form:

$6.47870866 \dots$

Related Questions