Basic Math Examples

\sqrt{50} - 2 \sqrt{18}

$\sqrt{50} - 2 \sqrt{18}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

50

$50$ as

5^{2} \cdot 2

$5^{2} \cdot 2$ .

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Step 1.1.1

Factor

25

$25$ out of

50

$50$ .

\sqrt{25 (2)} - 2 \sqrt{18}

$\sqrt{25 (2)} - 2 \sqrt{18}$

Step 1.1.2

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

\sqrt{5^{2} \cdot 2} - 2 \sqrt{18}

$\sqrt{5^{2} \cdot 2} - 2 \sqrt{18}$

\sqrt{5^{2} \cdot 2} - 2 \sqrt{18}

$\sqrt{5^{2} \cdot 2} - 2 \sqrt{18}$

Step 1.2

Pull terms out from under the radical.

5 \sqrt{2} - 2 \sqrt{18}

$5 \sqrt{2} - 2 \sqrt{18}$

Step 1.3

Rewrite

18

$18$ as

3^{2} \cdot 2

$3^{2} \cdot 2$ .

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Step 1.3.1

Factor

9

$9$ out of

18

$18$ .

5 \sqrt{2} - 2 \sqrt{9 (2)}

$5 \sqrt{2} - 2 \sqrt{9 (2)}$

Step 1.3.2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

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

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

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

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

Step 1.4

Pull terms out from under the radical.

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

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

Step 1.5

Multiply

3

$3$ by

- 2

$- 2$ .

5 \sqrt{2} - 6 \sqrt{2}

$5 \sqrt{2} - 6 \sqrt{2}$

5 \sqrt{2} - 6 \sqrt{2}

$5 \sqrt{2} - 6 \sqrt{2}$

Step 2

Subtract

6 \sqrt{2}

$6 \sqrt{2}$ from

5 \sqrt{2}

$5 \sqrt{2}$ .

- \sqrt{2}

$- \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

- \sqrt{2}

$- \sqrt{2}$

Decimal Form:

- 1.41421356 \dots

$- 1.41421356 \dots$

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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