Finite Math Examples

$\sqrt{27 x} - \sqrt{80 x} + \sqrt{20 x}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite $27 x$ as $3^{2} \cdot (3 x)$ .

Tap for more steps...

Step 1.1.1

Factor $9$ out of $27$ .

$\sqrt{9 (3) x} - \sqrt{80 x} + \sqrt{20 x}$

Step 1.1.2

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

$\sqrt{3^{2} \cdot 3 x} - \sqrt{80 x} + \sqrt{20 x}$

Step 1.1.3

Add parentheses.

$\sqrt{3^{2} \cdot (3 x)} - \sqrt{80 x} + \sqrt{20 x}$

Step 1.2

Pull terms out from under the radical.

$3 \sqrt{3 x} - \sqrt{80 x} + \sqrt{20 x}$

Step 1.3

Rewrite $80 x$ as ${(2^{2})}^{2} \cdot (5 x)$ .

Tap for more steps...

Step 1.3.1

Factor $16$ out of $80$ .

$3 \sqrt{3 x} - \sqrt{16 (5) x} + \sqrt{20 x}$

Step 1.3.2

Rewrite $16$ as $4^{2}$ .

$3 \sqrt{3 x} - \sqrt{4^{2} \cdot 5 x} + \sqrt{20 x}$

Step 1.3.3

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

$3 \sqrt{3 x} - \sqrt{{(2^{2})}^{2} \cdot 5 x} + \sqrt{20 x}$

Step 1.3.4

Add parentheses.

$3 \sqrt{3 x} - \sqrt{{(2^{2})}^{2} \cdot (5 x)} + \sqrt{20 x}$

Step 1.4

Pull terms out from under the radical.

$3 \sqrt{3 x} - (2^{2} \sqrt{5 x}) + \sqrt{20 x}$

Step 1.5

Raise $2$ to the power of $2$ .

$3 \sqrt{3 x} - (4 \sqrt{5 x}) + \sqrt{20 x}$

Step 1.6

Multiply $4$ by $- 1$ .

$3 \sqrt{3 x} - 4 \sqrt{5 x} + \sqrt{20 x}$

Step 1.7

Rewrite $20 x$ as $2^{2} \cdot (5 x)$ .

Tap for more steps...

Step 1.7.1

Factor $4$ out of $20$ .

$3 \sqrt{3 x} - 4 \sqrt{5 x} + \sqrt{4 (5) x}$

Step 1.7.2

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

$3 \sqrt{3 x} - 4 \sqrt{5 x} + \sqrt{2^{2} \cdot 5 x}$

Step 1.7.3

Add parentheses.

$3 \sqrt{3 x} - 4 \sqrt{5 x} + \sqrt{2^{2} \cdot (5 x)}$

Step 1.8

Pull terms out from under the radical.

$3 \sqrt{3 x} - 4 \sqrt{5 x} + 2 \sqrt{5 x}$

Step 2

Add $- 4 \sqrt{5 x}$ and $2 \sqrt{5 x}$ .

$3 \sqrt{3 x} - 2 \sqrt{5 x}$