Algebra Examples

- \sqrt{64} - \sqrt{- 50} + \sqrt{36} - \sqrt{- 32}

$- \sqrt{64} - \sqrt{- 50} + \sqrt{36} - \sqrt{- 32}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

64

$64$ as

8^{2}

$8^{2}$ .

- \sqrt{8^{2}} - \sqrt{- 50} + \sqrt{36} - \sqrt{- 32}

$- \sqrt{8^{2}} - \sqrt{- 50} + \sqrt{36} - \sqrt{- 32}$

Step 1.2

Pull terms out from under the radical.

- | 8 | - \sqrt{- 50} + \sqrt{36} - \sqrt{- 32}

$- | 8 | - \sqrt{- 50} + \sqrt{36} - \sqrt{- 32}$

Step 1.3

The absolute value is the distance between a number and zero. The distance between

0

$0$ and

8

$8$ is

8

$8$ .

- 1 \cdot 8 - \sqrt{- 50} + \sqrt{36} - \sqrt{- 32}

$- 1 \cdot 8 - \sqrt{- 50} + \sqrt{36} - \sqrt{- 32}$

Step 1.4

Multiply

- 1

$- 1$ by

8

$8$ .

- 8 - \sqrt{- 50} + \sqrt{36} - \sqrt{- 32}

$- 8 - \sqrt{- 50} + \sqrt{36} - \sqrt{- 32}$

Step 1.5

Rewrite

- 50

$- 50$ as

- 1 (50)

$- 1 (50)$ .

- 8 - \sqrt{- 1 (50)} + \sqrt{36} - \sqrt{- 32}

$- 8 - \sqrt{- 1 (50)} + \sqrt{36} - \sqrt{- 32}$

Step 1.6

Rewrite

\sqrt{- 1 (50)}

$\sqrt{- 1 (50)}$ as

\sqrt{- 1} \cdot \sqrt{50}

$\sqrt{- 1} \cdot \sqrt{50}$ .

- 8 - (\sqrt{- 1} \cdot \sqrt{50}) + \sqrt{36} - \sqrt{- 32}

$- 8 - (\sqrt{- 1} \cdot \sqrt{50}) + \sqrt{36} - \sqrt{- 32}$

Step 1.7

Rewrite

\sqrt{- 1}

$\sqrt{- 1}$ as

i

$i$ .

- 8 - (i \cdot \sqrt{50}) + \sqrt{36} - \sqrt{- 32}

$- 8 - (i \cdot \sqrt{50}) + \sqrt{36} - \sqrt{- 32}$

Step 1.8

Rewrite

50

$50$ as

5^{2} \cdot 2

$5^{2} \cdot 2$ .

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Step 1.8.1

Factor

25

$25$ out of

50

$50$ .

- 8 - (i \cdot \sqrt{25 (2)}) + \sqrt{36} - \sqrt{- 32}

$- 8 - (i \cdot \sqrt{25 (2)}) + \sqrt{36} - \sqrt{- 32}$

Step 1.8.2

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

- 8 - (i \cdot \sqrt{5^{2} \cdot 2}) + \sqrt{36} - \sqrt{- 32}

$- 8 - (i \cdot \sqrt{5^{2} \cdot 2}) + \sqrt{36} - \sqrt{- 32}$

- 8 - (i \cdot \sqrt{5^{2} \cdot 2}) + \sqrt{36} - \sqrt{- 32}

$- 8 - (i \cdot \sqrt{5^{2} \cdot 2}) + \sqrt{36} - \sqrt{- 32}$

Step 1.9

Pull terms out from under the radical.

- 8 - (i \cdot (| 5 | \sqrt{2})) + \sqrt{36} - \sqrt{- 32}

$- 8 - (i \cdot (| 5 | \sqrt{2})) + \sqrt{36} - \sqrt{- 32}$

Step 1.10

The absolute value is the distance between a number and zero. The distance between

0

$0$ and

5

$5$ is

5

$5$ .

- 8 - (i \cdot (5 \sqrt{2})) + \sqrt{36} - \sqrt{- 32}

$- 8 - (i \cdot (5 \sqrt{2})) + \sqrt{36} - \sqrt{- 32}$

Step 1.11

Move

5

$5$ to the left of

i

$i$ .

- 8 - (5 \cdot i \sqrt{2}) + \sqrt{36} - \sqrt{- 32}

$- 8 - (5 \cdot i \sqrt{2}) + \sqrt{36} - \sqrt{- 32}$

Step 1.12

Multiply

5

$5$ by

- 1

$- 1$ .

- 8 - 5 (i \sqrt{2}) + \sqrt{36} - \sqrt{- 32}

$- 8 - 5 (i \sqrt{2}) + \sqrt{36} - \sqrt{- 32}$

Step 1.13

Rewrite

36

$36$ as

6^{2}

$6^{2}$ .

- 8 - 5 i \sqrt{2} + \sqrt{6^{2}} - \sqrt{- 32}

$- 8 - 5 i \sqrt{2} + \sqrt{6^{2}} - \sqrt{- 32}$

Step 1.14

Pull terms out from under the radical.

- 8 - 5 i \sqrt{2} + | 6 | - \sqrt{- 32}

$- 8 - 5 i \sqrt{2} + | 6 | - \sqrt{- 32}$

Step 1.15

The absolute value is the distance between a number and zero. The distance between

0

$0$ and

6

$6$ is

6

$6$ .

- 8 - 5 i \sqrt{2} + 6 - \sqrt{- 32}

$- 8 - 5 i \sqrt{2} + 6 - \sqrt{- 32}$

Step 1.16

Rewrite

- 32

$- 32$ as

- 1 (32)

$- 1 (32)$ .

- 8 - 5 i \sqrt{2} + 6 - \sqrt{- 1 (32)}

$- 8 - 5 i \sqrt{2} + 6 - \sqrt{- 1 (32)}$

Step 1.17

Rewrite

\sqrt{- 1 (32)}

$\sqrt{- 1 (32)}$ as

\sqrt{- 1} \cdot \sqrt{32}

$\sqrt{- 1} \cdot \sqrt{32}$ .

- 8 - 5 i \sqrt{2} + 6 - (\sqrt{- 1} \cdot \sqrt{32})

$- 8 - 5 i \sqrt{2} + 6 - (\sqrt{- 1} \cdot \sqrt{32})$

Step 1.18

Rewrite

\sqrt{- 1}

$\sqrt{- 1}$ as

i

$i$ .

- 8 - 5 i \sqrt{2} + 6 - (i \cdot \sqrt{32})

$- 8 - 5 i \sqrt{2} + 6 - (i \cdot \sqrt{32})$

Step 1.19

Rewrite

$32$ as

$4^{2} \cdot 2$ .

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Step 1.19.1

Factor

$16$ out of

$32$ .

$- 8 - 5 i \sqrt{2} + 6 - (i \cdot \sqrt{16 (2)})$

Step 1.19.2

Rewrite

$16$ as

$4^{2}$ .

$- 8 - 5 i \sqrt{2} + 6 - (i \cdot \sqrt{4^{2} \cdot 2})$

Step 1.20

Pull terms out from under the radical.

$- 8 - 5 i \sqrt{2} + 6 - (i \cdot (| 4 | \sqrt{2}))$

Step 1.21

The absolute value is the distance between a number and zero. The distance between

$0$ and

$4$ is

$4$ .

$- 8 - 5 i \sqrt{2} + 6 - (i \cdot (4 \sqrt{2}))$

Step 1.22

Move

$4$ to the left of

$i$ .

$- 8 - 5 i \sqrt{2} + 6 - (4 \cdot i \sqrt{2})$

Step 1.23

Multiply

$4$ by

$- 1$ .

$- 8 - 5 i \sqrt{2} + 6 - 4 i \sqrt{2}$

Step 2

Add

$- 8$ and

$6$ .

$- 5 i \sqrt{2} - 2 - 4 i \sqrt{2}$

Step 3

Subtract

$4 i \sqrt{2}$ from

$- 5 i \sqrt{2}$ .

$- 9 i \sqrt{2} - 2$

Step 4

Reorder

$- 9 i \sqrt{2}$ and

$- 2$ .

$- 2 - 9 i \sqrt{2}$