Basic Math Examples

2^{4} \cdot (5 + \sqrt{\frac{36}{3}})

$2^{4} \cdot (5 + \sqrt{\frac{36}{3}})$

Step 1

Raise

2

$2$ to the power of

4

$4$ .

16 \cdot (5 + \sqrt{\frac{36}{3}})

$16 \cdot (5 + \sqrt{\frac{36}{3}})$

Step 2

Simplify each term.

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Step 2.1

Divide

36

$36$ by

3

$3$ .

16 \cdot (5 + \sqrt{12})

$16 \cdot (5 + \sqrt{12})$

Step 2.2

Rewrite

12

$12$ as

2^{2} \cdot 3

$2^{2} \cdot 3$ .

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Step 2.2.1

Factor

4

$4$ out of

12

$12$ .

16 \cdot (5 + \sqrt{4 (3)})

$16 \cdot (5 + \sqrt{4 (3)})$

Step 2.2.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

16 \cdot (5 + \sqrt{2^{2} \cdot 3})

$16 \cdot (5 + \sqrt{2^{2} \cdot 3})$

16 \cdot (5 + \sqrt{2^{2} \cdot 3})

$16 \cdot (5 + \sqrt{2^{2} \cdot 3})$

Step 2.3

Pull terms out from under the radical.

16 \cdot (5 + 2 \sqrt{3})

$16 \cdot (5 + 2 \sqrt{3})$

16 \cdot (5 + 2 \sqrt{3})

$16 \cdot (5 + 2 \sqrt{3})$

Step 3

Simplify by multiplying through.

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Step 3.1

Apply the distributive property.

16 \cdot 5 + 16 (2 \sqrt{3})

$16 \cdot 5 + 16 (2 \sqrt{3})$

Step 3.2

Multiply.

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Step 3.2.1

Multiply

$16$ by

$5$ .

$80 + 16 (2 \sqrt{3})$

Step 3.2.2

Multiply

$2$ by

$16$ .

$80 + 32 \sqrt{3}$

$80 + 32 \sqrt{3}$

$80 + 32 \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$80 + 32 \sqrt{3}$

Decimal Form:

$135.42562584 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$