Algebra Examples

\sqrt{- 72}

$\sqrt{- 72}$

Step 1

Rewrite

- 72

$- 72$ as

- 1 (72)

$- 1 (72)$ .

\sqrt{- 1 (72)}

$\sqrt{- 1 (72)}$

Step 2

Rewrite

\sqrt{- 1 (72)}

$\sqrt{- 1 (72)}$ as

\sqrt{- 1} \cdot \sqrt{72}

$\sqrt{- 1} \cdot \sqrt{72}$ .

\sqrt{- 1} \cdot \sqrt{72}

$\sqrt{- 1} \cdot \sqrt{72}$

Step 3

Rewrite

\sqrt{- 1}

$\sqrt{- 1}$ as

i

$i$ .

i \cdot \sqrt{72}

$i \cdot \sqrt{72}$

Step 4

Rewrite

72

$72$ as

6^{2} \cdot 2

$6^{2} \cdot 2$ .

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Step 4.1

Factor

36

$36$ out of

72

$72$ .

i \cdot \sqrt{36 (2)}

$i \cdot \sqrt{36 (2)}$

Step 4.2

Rewrite

36

$36$ as

6^{2}

$6^{2}$ .

i \cdot \sqrt{6^{2} \cdot 2}

$i \cdot \sqrt{6^{2} \cdot 2}$

i \cdot \sqrt{6^{2} \cdot 2}

$i \cdot \sqrt{6^{2} \cdot 2}$

Step 5

Pull terms out from under the radical.

i \cdot (6 \sqrt{2})

$i \cdot (6 \sqrt{2})$

Step 6

Move

6

$6$ to the left of

i

$i$ .

6 i \sqrt{2}

$6 i \sqrt{2}$

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

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