Basic Math Examples

9 \sqrt{50} + \sqrt{98}

$9 \sqrt{50} + \sqrt{98}$

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

$50$ .

9 \sqrt{25 (2)} + \sqrt{98}

$9 \sqrt{25 (2)} + \sqrt{98}$

Step 1.1.2

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

9 \sqrt{5^{2} \cdot 2} + \sqrt{98}

$9 \sqrt{5^{2} \cdot 2} + \sqrt{98}$

9 \sqrt{5^{2} \cdot 2} + \sqrt{98}

$9 \sqrt{5^{2} \cdot 2} + \sqrt{98}$

Step 1.2

Pull terms out from under the radical.

9 (5 \sqrt{2}) + \sqrt{98}

$9 (5 \sqrt{2}) + \sqrt{98}$

Step 1.3

Multiply

5

$5$ by

9

$9$ .

45 \sqrt{2} + \sqrt{98}

$45 \sqrt{2} + \sqrt{98}$

Step 1.4

Rewrite

98

$98$ as

7^{2} \cdot 2

$7^{2} \cdot 2$ .

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Step 1.4.1

Factor

49

$49$ out of

98

$98$ .

45 \sqrt{2} + \sqrt{49 (2)}

$45 \sqrt{2} + \sqrt{49 (2)}$

Step 1.4.2

Rewrite

49

$49$ as

7^{2}

$7^{2}$ .

45 \sqrt{2} + \sqrt{7^{2} \cdot 2}

$45 \sqrt{2} + \sqrt{7^{2} \cdot 2}$

45 \sqrt{2} + \sqrt{7^{2} \cdot 2}

$45 \sqrt{2} + \sqrt{7^{2} \cdot 2}$

Step 1.5

Pull terms out from under the radical.

45 \sqrt{2} + 7 \sqrt{2}

$45 \sqrt{2} + 7 \sqrt{2}$

45 \sqrt{2} + 7 \sqrt{2}

$45 \sqrt{2} + 7 \sqrt{2}$

Step 2

Add

45 \sqrt{2}

$45 \sqrt{2}$ and

7 \sqrt{2}

$7 \sqrt{2}$ .

52 \sqrt{2}

$52 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

52 \sqrt{2}

$52 \sqrt{2}$

Decimal Form:

73.53910524 \dots

$73.53910524 \dots$

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

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