Simplify square root of 45- square root of 27- square root of 20

$\sqrt{45} - \sqrt{27} - \sqrt{20}$

Step 1

Simplify each term.

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

Factor $9$ out of $45$ .

$\sqrt{9 (5)} - \sqrt{27} - \sqrt{20}$

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

$\sqrt{3^{2} \cdot 5} - \sqrt{27} - \sqrt{20}$

$\sqrt{3^{2} \cdot 5} - \sqrt{27} - \sqrt{20}$

Pull terms out from under the radical.

$3 \sqrt{5} - \sqrt{27} - \sqrt{20}$

Rewrite $27$ as $3^{2} \cdot 3$ .

Factor $9$ out of $27$ .

$3 \sqrt{5} - \sqrt{9 (3)} - \sqrt{20}$

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

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

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

Pull terms out from under the radical.

$3 \sqrt{5} - (3 \sqrt{3}) - \sqrt{20}$

Multiply $3$ by $- 1$ .

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

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

Factor $4$ out of $20$ .

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

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 1$ .

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

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

Step 2

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

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 2.96008444 \dots$

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