Simplify the Radical Expression 10 square root of 10+10 square root of 40

$10 \sqrt{10} + 10 \sqrt{40}$

Simplify each term.

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

$10 \sqrt{10} + 10 \sqrt{4 (10)}$

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

$10 \sqrt{10} + 10 \sqrt{2^{2} \cdot 10}$

Pull terms out from under the radical.

$10 \sqrt{10} + 10 (| 2 | \sqrt{10})$

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

$10 \sqrt{10} + 10 (2 \sqrt{10})$

Multiply $2$ by $10$ .

$10 \sqrt{10} + 20 \sqrt{10}$

Add $10 \sqrt{10}$ and $20 \sqrt{10}$ .

$30 \sqrt{10}$

The result can be shown in multiple forms.

Exact Form:

$30 \sqrt{10}$

Decimal Form:

$94.86832980 \dots$