Simplify the Radical Expression square root of 175- square root of 28

$\sqrt{175} - \sqrt{28}$

Simplify each term.

Rewrite $175$ as $5^{2} \cdot 7$ .

Factor $25$ out of $175$ .

$\sqrt{25 (7)} - \sqrt{28}$

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

$\sqrt{5^{2} \cdot 7} - \sqrt{28}$

Pull terms out from under the radical.

$| 5 | \sqrt{7} - \sqrt{28}$

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

$5 \sqrt{7} - \sqrt{28}$

Rewrite $28$ as $2^{2} \cdot 7$ .

Factor $4$ out of $28$ .

$5 \sqrt{7} - \sqrt{4 (7)}$

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

$5 \sqrt{7} - \sqrt{2^{2} \cdot 7}$

Pull terms out from under the radical.

$5 \sqrt{7} - (| 2 | \sqrt{7})$

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

$5 \sqrt{7} - (2 \sqrt{7})$

Multiply $2$ by $- 1$ .

$5 \sqrt{7} - 2 \sqrt{7}$

Subtract $2 \sqrt{7}$ from $5 \sqrt{7}$ .

$3 \sqrt{7}$

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{7}$

Decimal Form:

$7.93725393 \dots$