Basic Math Examples

$\frac{7 \sqrt{5}}{3} - \frac{\sqrt{45}}{3}$

Step 1

Combine the numerators over the common denominator.

$\frac{7 \sqrt{5} - \sqrt{45}}{3}$

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Factor $9$ out of $45$ .

$\frac{7 \sqrt{5} - \sqrt{9 (5)}}{3}$

Step 2.1.2

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

$\frac{7 \sqrt{5} - \sqrt{3^{2} \cdot 5}}{3}$

$\frac{7 \sqrt{5} - \sqrt{3^{2} \cdot 5}}{3}$

Step 2.2

Pull terms out from under the radical.

$\frac{7 \sqrt{5} - (3 \sqrt{5})}{3}$

Step 2.3

Multiply $3$ by $- 1$ .

$\frac{7 \sqrt{5} - 3 \sqrt{5}}{3}$

$\frac{7 \sqrt{5} - 3 \sqrt{5}}{3}$

Step 3

Subtract $3 \sqrt{5}$ from $7 \sqrt{5}$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$2.98142397 \dots$

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