Basic Math Examples

$\sqrt{5}$ , $\sqrt{12 \sqrt{13}}$

Step 1

Arrange the terms in ascending order.

$\sqrt{5}, \sqrt{12 \sqrt{13}}$

Step 2

The median is the middle term in the arranged data set. In the case of an even number of terms, the median is the average of the two middle terms.

$\frac{\sqrt{5} + \sqrt{12 \sqrt{13}}}{2}$

Step 3

Remove parentheses.

$\frac{\sqrt{5} + \sqrt{12 \sqrt{13}}}{2}$

Step 4

Simplify the numerator.

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Step 4.1

Rewrite $12 \sqrt{13}$ as $2^{2} \cdot (3 \sqrt{13})$ .

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Step 4.1.1

Factor $4$ out of $12$ .

$\frac{\sqrt{5} + \sqrt{4 (3) \sqrt{13}}}{2}$

Step 4.1.2

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

$\frac{\sqrt{5} + \sqrt{2^{2} \cdot 3 \sqrt{13}}}{2}$

Step 4.1.3

Add parentheses.

$\frac{\sqrt{5} + \sqrt{2^{2} \cdot (3 \sqrt{13})}}{2}$

Step 4.2

Pull terms out from under the radical.

$\frac{\sqrt{5} + 2 \sqrt{3 \sqrt{13}}}{2}$

Step 5

Convert the median $\frac{\sqrt{5} + 2 \sqrt{3 \sqrt{13}}}{2}$ to decimal.

$4.40690215$