Basic Math Examples

$3 \sqrt{147} + \sqrt{245}$

Step 1

Rewrite $147$ as $7^{2} \cdot 3$ .

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Step 1.1

Factor $49$ out of $147$ .

$3 \sqrt{49 (3)} + \sqrt{245}$

Step 1.2

Rewrite $49$ as $7^{2}$ .

$3 \sqrt{7^{2} \cdot 3} + \sqrt{245}$

$3 \sqrt{7^{2} \cdot 3} + \sqrt{245}$

Step 2

Pull terms out from under the radical.

$3 (7 \sqrt{3}) + \sqrt{245}$

Step 3

Multiply $7$ by $3$ .

$21 \sqrt{3} + \sqrt{245}$

Step 4

Rewrite $245$ as $7^{2} \cdot 5$ .

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Step 4.1

Factor $49$ out of $245$ .

$21 \sqrt{3} + \sqrt{49 (5)}$

Step 4.2

Rewrite $49$ as $7^{2}$ .

$21 \sqrt{3} + \sqrt{7^{2} \cdot 5}$

$21 \sqrt{3} + \sqrt{7^{2} \cdot 5}$

Step 5

Pull terms out from under the radical.

$21 \sqrt{3} + 7 \sqrt{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$21 \sqrt{3} + 7 \sqrt{5}$

Decimal Form:

$52.02554280 \dots$

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