Basic Math Examples

3 \sqrt{294 \cdot \sqrt{42}}

$3 \sqrt{294 \cdot \sqrt{42}}$

Step 1

Rewrite

294 \cdot \sqrt{42}

$294 \cdot \sqrt{42}$ as

7^{2} \cdot (6 \cdot \sqrt{42})

$7^{2} \cdot (6 \cdot \sqrt{42})$ .

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Step 1.1

Factor

49

$49$ out of

294

$294$ .

3 \sqrt{49 (6) \cdot \sqrt{42}}

$3 \sqrt{49 (6) \cdot \sqrt{42}}$

Step 1.2

Rewrite

49

$49$ as

7^{2}

$7^{2}$ .

3 \sqrt{7^{2} \cdot 6 \cdot \sqrt{42}}

$3 \sqrt{7^{2} \cdot 6 \cdot \sqrt{42}}$

Step 1.3

Add parentheses.

3 \sqrt{7^{2} \cdot (6 \cdot \sqrt{42})}

$3 \sqrt{7^{2} \cdot (6 \cdot \sqrt{42})}$

3 \sqrt{7^{2} \cdot (6 \cdot \sqrt{42})}

$3 \sqrt{7^{2} \cdot (6 \cdot \sqrt{42})}$

Step 2

Pull terms out from under the radical.

3 (7 \sqrt{6 \cdot \sqrt{42}})

$3 (7 \sqrt{6 \cdot \sqrt{42}})$

Step 3

Multiply

7

$7$ by

3

$3$ .

21 \sqrt{6 \cdot \sqrt{42}}

$21 \sqrt{6 \cdot \sqrt{42}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

21 \sqrt{6 \cdot \sqrt{42}}

$21 \sqrt{6 \cdot \sqrt{42}}$

Decimal Form:

130.95052458 \dots

$130.95052458 \dots$

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

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