Algebra Examples

$\sqrt{80} - \sqrt{45}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $80$ as $4^{2} \cdot 5$ .

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Step 1.1.1

Factor $16$ out of $80$ .

$\sqrt{16 (5)} - \sqrt{45}$

Step 1.1.2

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

$\sqrt{4^{2} \cdot 5} - \sqrt{45}$

$\sqrt{4^{2} \cdot 5} - \sqrt{45}$

Step 1.2

Pull terms out from under the radical.

$4 \sqrt{5} - \sqrt{45}$

Step 1.3

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

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Step 1.3.1

Factor $9$ out of $45$ .

$4 \sqrt{5} - \sqrt{9 (5)}$

Step 1.3.2

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

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

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

Step 1.4

Pull terms out from under the radical.

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

Step 1.5

Multiply $3$ by $- 1$ .

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

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

Step 2

Subtract $3 \sqrt{5}$ from $4 \sqrt{5}$ .

$\sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{5}$

Decimal Form:

$2.23606797 \dots$

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