Basic Math Examples

$\sqrt[4]{81} - 8 \sqrt[3]{216} + 15 \sqrt[5]{32} + \sqrt{225}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $81$ as $3^{4}$ .

$\sqrt[4]{3^{4}} - 8 \sqrt[3]{216} + 15 \sqrt[5]{32} + \sqrt{225}$

Step 1.2

Pull terms out from under the radical, assuming positive real numbers.

$3 - 8 \sqrt[3]{216} + 15 \sqrt[5]{32} + \sqrt{225}$

Step 1.3

Rewrite $216$ as $6^{3}$ .

$3 - 8 \sqrt[3]{6^{3}} + 15 \sqrt[5]{32} + \sqrt{225}$

Step 1.4

Pull terms out from under the radical, assuming real numbers.

$3 - 8 \cdot 6 + 15 \sqrt[5]{32} + \sqrt{225}$

Step 1.5

Multiply $- 8$ by $6$ .

$3 - 48 + 15 \sqrt[5]{32} + \sqrt{225}$

Step 1.6

Rewrite $32$ as $2^{5}$ .

$3 - 48 + 15 \sqrt[5]{2^{5}} + \sqrt{225}$

Step 1.7

Pull terms out from under the radical, assuming real numbers.

$3 - 48 + 15 \cdot 2 + \sqrt{225}$

Step 1.8

Multiply $15$ by $2$ .

$3 - 48 + 30 + \sqrt{225}$

Step 1.9

Rewrite $225$ as $15^{2}$ .

$3 - 48 + 30 + \sqrt{15^{2}}$

Step 1.10

Pull terms out from under the radical, assuming positive real numbers.

$3 - 48 + 30 + 15$

Step 2

Simplify by adding and subtracting.

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Step 2.1

Subtract $48$ from $3$ .

$- 45 + 30 + 15$

Step 2.2

Add $- 45$ and $30$ .

$- 15 + 15$

Step 2.3

Add $- 15$ and $15$ .

$0$