Pre-Algebra Examples

$\sqrt{45} - 3 \sqrt{20}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite $45$ as $3^{2} \cdot 5$ .

Tap for more steps...

Step 1.1.1

Factor $9$ out of $45$ .

$\sqrt{9 (5)} - 3 \sqrt{20}$

Step 1.1.2

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

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

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

Step 1.2

Pull terms out from under the radical.

$3 \sqrt{5} - 3 \sqrt{20}$

Step 1.3

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

Tap for more steps...

Step 1.3.1

Factor $4$ out of $20$ .

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

Step 1.3.2

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

$3 \sqrt{5} - 3 \sqrt{2^{2} \cdot 5}$

$3 \sqrt{5} - 3 \sqrt{2^{2} \cdot 5}$

Step 1.4

Pull terms out from under the radical.

$3 \sqrt{5} - 3 (2 \sqrt{5})$

Step 1.5

Multiply $2$ by $- 3$ .

$3 \sqrt{5} - 6 \sqrt{5}$

$3 \sqrt{5} - 6 \sqrt{5}$

Step 2

Subtract $6 \sqrt{5}$ from $3 \sqrt{5}$ .

$- 3 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 3 \sqrt{5}$

Decimal Form:

$- 6.70820393 \dots$

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