Simplify square root of 320+ square root of 45+ cube root of 40

$\sqrt{320} + \sqrt{45} + \sqrt[3]{40}$

Step 1

Simplify each term.

Rewrite $320$ as $8^{2} \cdot 5$ .

Factor $64$ out of $320$ .

$\sqrt{64 (5)} + \sqrt{45} + \sqrt[3]{40}$

Rewrite $64$ as $8^{2}$ .

$\sqrt{8^{2} \cdot 5} + \sqrt{45} + \sqrt[3]{40}$

Pull terms out from under the radical.

$8 \sqrt{5} + \sqrt{45} + \sqrt[3]{40}$

Rewrite $45$ as $3^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$8 \sqrt{5} + \sqrt{9 (5)} + \sqrt[3]{40}$

Rewrite $9$ as $3^{2}$ .

$8 \sqrt{5} + \sqrt{3^{2} \cdot 5} + \sqrt[3]{40}$

Pull terms out from under the radical.

$8 \sqrt{5} + 3 \sqrt{5} + \sqrt[3]{40}$

Rewrite $40$ as $2^{3} \cdot 5$ .

Factor $8$ out of $40$ .

$8 \sqrt{5} + 3 \sqrt{5} + \sqrt[3]{8 (5)}$

Rewrite $8$ as $2^{3}$ .

$8 \sqrt{5} + 3 \sqrt{5} + \sqrt[3]{2^{3} \cdot 5}$

Pull terms out from under the radical.

$8 \sqrt{5} + 3 \sqrt{5} + 2 \sqrt[3]{5}$

Step 2

Add $8 \sqrt{5}$ and $3 \sqrt{5}$ .

$11 \sqrt{5} + 2 \sqrt[3]{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$11 \sqrt{5} + 2 \sqrt[3]{5}$

Decimal Form:

$28.01669964 \dots$