Algebra Examples

$4 \sqrt{n^{2}} + \sqrt{m^{2} n} - \sqrt{4 n^{2}} - \sqrt{m n^{2}}$

Step 1

Simplify each term.

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Step 1.1

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

$4 n + \sqrt{m^{2} n} - \sqrt{4 n^{2}} - \sqrt{m n^{2}}$

Step 1.2

Pull terms out from under the radical.

$4 n + m \sqrt{n} - \sqrt{4 n^{2}} - \sqrt{m n^{2}}$

Step 1.3

Rewrite $4 n^{2}$ as ${(2 n)}^{2}$ .

$4 n + m \sqrt{n} - \sqrt{{(2 n)}^{2}} - \sqrt{m n^{2}}$

Step 1.4

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

$4 n + m \sqrt{n} - (2 n) - \sqrt{m n^{2}}$

Step 1.5

Multiply $2$ by $- 1$ .

$4 n + m \sqrt{n} - 2 n - \sqrt{m n^{2}}$

Step 1.6

Reorder $m$ and $n^{2}$ .

$4 n + m \sqrt{n} - 2 n - \sqrt{n^{2} m}$

Step 1.7

Pull terms out from under the radical.

$4 n + m \sqrt{n} - 2 n - n \sqrt{m}$

Step 2

Subtract $2 n$ from $4 n$ .

$m \sqrt{n} + 2 n - n \sqrt{m}$