Simplify the Radical Expression square root of 20+ square root of 48-3 square root of 125

$\sqrt{20} + \sqrt{48} - 3 \sqrt{125}$

Step 1

Simplify each term.

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

Factor $4$ out of $20$ .

$\sqrt{4 (5)} + \sqrt{48} - 3 \sqrt{125}$

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

$\sqrt{2^{2} \cdot 5} + \sqrt{48} - 3 \sqrt{125}$

Pull terms out from under the radical.

$| 2 | \sqrt{5} + \sqrt{48} - 3 \sqrt{125}$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$2 \sqrt{5} + \sqrt{48} - 3 \sqrt{125}$

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$2 \sqrt{5} + \sqrt{16 (3)} - 3 \sqrt{125}$

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

$2 \sqrt{5} + \sqrt{4^{2} \cdot 3} - 3 \sqrt{125}$

Pull terms out from under the radical.

$2 \sqrt{5} + | 4 | \sqrt{3} - 3 \sqrt{125}$

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$2 \sqrt{5} + 4 \sqrt{3} - 3 \sqrt{125}$

Rewrite $125$ as $5^{2} \cdot 5$ .

Factor $25$ out of $125$ .

$2 \sqrt{5} + 4 \sqrt{3} - 3 \sqrt{25 (5)}$

Rewrite $25$ as $5^{2}$ .

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

Pull terms out from under the radical.

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

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

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

Multiply $5$ by $- 3$ .

$2 \sqrt{5} + 4 \sqrt{3} - 15 \sqrt{5}$

Step 2

Subtract $15 \sqrt{5}$ from $2 \sqrt{5}$ .

$- 13 \sqrt{5} + 4 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 13 \sqrt{5} + 4 \sqrt{3}$

Decimal Form:

$- 22.14068047 \dots$