Basic Math Examples

\sqrt{8} - \sqrt{98}

$\sqrt{8} - \sqrt{98}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

8

$8$ as

2^{2} \cdot 2

$2^{2} \cdot 2$ .

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Step 1.1.1

Factor

4

$4$ out of

8

$8$ .

\sqrt{4 (2)} - \sqrt{98}

$\sqrt{4 (2)} - \sqrt{98}$

Step 1.1.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

\sqrt{2^{2} \cdot 2} - \sqrt{98}

$\sqrt{2^{2} \cdot 2} - \sqrt{98}$

\sqrt{2^{2} \cdot 2} - \sqrt{98}

$\sqrt{2^{2} \cdot 2} - \sqrt{98}$

Step 1.2

Pull terms out from under the radical.

2 \sqrt{2} - \sqrt{98}

$2 \sqrt{2} - \sqrt{98}$

Step 1.3

Rewrite

98

$98$ as

7^{2} \cdot 2

$7^{2} \cdot 2$ .

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Step 1.3.1

Factor

49

$49$ out of

98

$98$ .

2 \sqrt{2} - \sqrt{49 (2)}

$2 \sqrt{2} - \sqrt{49 (2)}$

Step 1.3.2

Rewrite

49

$49$ as

7^{2}

$7^{2}$ .

2 \sqrt{2} - \sqrt{7^{2} \cdot 2}

$2 \sqrt{2} - \sqrt{7^{2} \cdot 2}$

2 \sqrt{2} - \sqrt{7^{2} \cdot 2}

$2 \sqrt{2} - \sqrt{7^{2} \cdot 2}$

Step 1.4

Pull terms out from under the radical.

2 \sqrt{2} - (7 \sqrt{2})

$2 \sqrt{2} - (7 \sqrt{2})$

Step 1.5

Multiply

7

$7$ by

- 1

$- 1$ .

2 \sqrt{2} - 7 \sqrt{2}

$2 \sqrt{2} - 7 \sqrt{2}$

2 \sqrt{2} - 7 \sqrt{2}

$2 \sqrt{2} - 7 \sqrt{2}$

Step 2

Subtract

7 \sqrt{2}

$7 \sqrt{2}$ from

2 \sqrt{2}

$2 \sqrt{2}$ .

- 5 \sqrt{2}

$- 5 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

- 5 \sqrt{2}

$- 5 \sqrt{2}$

Decimal Form:

- 7.07106781 \dots

$- 7.07106781 \dots$

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

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