Simplify square root of 5*2 square root of 32-21 square root of 10

$\sqrt{5} \cdot 2 \sqrt{32} - 21 \sqrt{10}$

Step 1

Simplify each term.

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

Factor $16$ out of $32$ .

$\sqrt{5} \cdot (2 \sqrt{16 (2)}) - 21 \sqrt{10}$

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

$\sqrt{5} \cdot (2 \sqrt{4^{2} \cdot 2}) - 21 \sqrt{10}$

Pull terms out from under the radical.

$\sqrt{5} \cdot (2 (4 \sqrt{2})) - 21 \sqrt{10}$

Multiply $4$ by $2$ .

$\sqrt{5} \cdot (8 \sqrt{2}) - 21 \sqrt{10}$

Multiply $\sqrt{5} (8 \sqrt{2})$ .

Combine using the product rule for radicals.

$8 \sqrt{5 \cdot 2} - 21 \sqrt{10}$

Multiply $5$ by $2$ .

$8 \sqrt{10} - 21 \sqrt{10}$

Step 2

Subtract $21 \sqrt{10}$ from $8 \sqrt{10}$ .

$- 13 \sqrt{10}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 13 \sqrt{10}$

Decimal Form:

$- 41.10960958 \dots$