Evaluate square root of 50- square root of 32

$\sqrt{50} - \sqrt{32}$

Step 1

Simplify each term.

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$\sqrt{25 (2)} - \sqrt{32}$

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

$\sqrt{5^{2} \cdot 2} - \sqrt{32}$

$\sqrt{5^{2} \cdot 2} - \sqrt{32}$

Pull terms out from under the radical.

$5 \sqrt{2} - \sqrt{32}$

Rewrite $32$ as $4^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$5 \sqrt{2} - \sqrt{16 (2)}$

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

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

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

Pull terms out from under the radical.

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

Multiply $4$ by $- 1$ .

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

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

Step 2

Subtract $4 \sqrt{2}$ from $5 \sqrt{2}$ .

$\sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2}$

Decimal Form:

$1.41421356 \dots$

Related Questions