Basic Math Examples

$\frac{3}{2} \cdot \sqrt{80} + 2 \sqrt{24} - \frac{1}{5} \cdot \sqrt{125}$

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 $80$ .

$\frac{3}{2} \cdot \sqrt{16 (5)} + 2 \sqrt{24} - \frac{1}{5} \cdot \sqrt{125}$

Step 1.1.2

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

$\frac{3}{2} \cdot \sqrt{4^{2} \cdot 5} + 2 \sqrt{24} - \frac{1}{5} \cdot \sqrt{125}$

Step 1.2

Pull terms out from under the radical.

$\frac{3}{2} \cdot (4 \sqrt{5}) + 2 \sqrt{24} - \frac{1}{5} \cdot \sqrt{125}$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $4 \sqrt{5}$ .

$\frac{3}{2} \cdot (2 (2 \sqrt{5})) + 2 \sqrt{24} - \frac{1}{5} \cdot \sqrt{125}$

Step 1.3.2

Cancel the common factor.

$\frac{3}{2} \cdot (2 (2 \sqrt{5})) + 2 \sqrt{24} - \frac{1}{5} \cdot \sqrt{125}$

Step 1.3.3

Rewrite the expression.

$3 \cdot (2 \sqrt{5}) + 2 \sqrt{24} - \frac{1}{5} \cdot \sqrt{125}$

Step 1.4

Multiply $2$ by $3$ .

$6 \cdot \sqrt{5} + 2 \sqrt{24} - \frac{1}{5} \cdot \sqrt{125}$

Step 1.5

Rewrite $24$ as $2^{2} \cdot 6$ .

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Step 1.5.1

Factor $4$ out of $24$ .

$6 \sqrt{5} + 2 \sqrt{4 (6)} - \frac{1}{5} \cdot \sqrt{125}$

Step 1.5.2

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

$6 \sqrt{5} + 2 \sqrt{2^{2} \cdot 6} - \frac{1}{5} \cdot \sqrt{125}$

Step 1.6

Pull terms out from under the radical.

$6 \sqrt{5} + 2 (2 \sqrt{6}) - \frac{1}{5} \cdot \sqrt{125}$

Step 1.7

Multiply $2$ by $2$ .

$6 \sqrt{5} + 4 \sqrt{6} - \frac{1}{5} \cdot \sqrt{125}$

Step 1.8

Rewrite $125$ as $5^{2} \cdot 5$ .

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Step 1.8.1

Factor $25$ out of $125$ .

$6 \sqrt{5} + 4 \sqrt{6} - \frac{1}{5} \cdot \sqrt{25 (5)}$

Step 1.8.2

Rewrite $25$ as $5^{2}$ .

$6 \sqrt{5} + 4 \sqrt{6} - \frac{1}{5} \cdot \sqrt{5^{2} \cdot 5}$

Step 1.9

Pull terms out from under the radical.

$6 \sqrt{5} + 4 \sqrt{6} - \frac{1}{5} \cdot (5 \sqrt{5})$

Step 1.10

Cancel the common factor of $5$ .

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Step 1.10.1

Move the leading negative in $- \frac{1}{5}$ into the numerator.

$6 \sqrt{5} + 4 \sqrt{6} + \frac{- 1}{5} \cdot (5 \sqrt{5})$

Step 1.10.2

Factor $5$ out of $5 \sqrt{5}$ .

$6 \sqrt{5} + 4 \sqrt{6} + \frac{- 1}{5} \cdot (5 (\sqrt{5}))$

Step 1.10.3

Cancel the common factor.

$6 \sqrt{5} + 4 \sqrt{6} + \frac{- 1}{5} \cdot (5 \sqrt{5})$

Step 1.10.4

Rewrite the expression.

$6 \sqrt{5} + 4 \sqrt{6} - 1 \cdot \sqrt{5}$

Step 1.11

Rewrite $- 1 \sqrt{5}$ as $- \sqrt{5}$ .

$6 \sqrt{5} + 4 \sqrt{6} - \sqrt{5}$

Step 2

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

$5 \sqrt{5} + 4 \sqrt{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{5} + 4 \sqrt{6}$

Decimal Form:

$20.97829885 \dots$