Algebra Examples

$\sqrt{144} - \sqrt{- 50} - \sqrt{49} - \sqrt{- 98}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $144$ as $12^{2}$ .

$\sqrt{12^{2}} - \sqrt{- 50} - \sqrt{49} - \sqrt{- 98}$

Step 1.2

Pull terms out from under the radical.

$| 12 | - \sqrt{- 50} - \sqrt{49} - \sqrt{- 98}$

Step 1.3

The absolute value is the distance between a number and zero. The distance between $0$ and $12$ is $12$ .

$12 - \sqrt{- 50} - \sqrt{49} - \sqrt{- 98}$

Step 1.4

Rewrite $- 50$ as $- 1 (50)$ .

$12 - \sqrt{- 1 (50)} - \sqrt{49} - \sqrt{- 98}$

Step 1.5

Rewrite $\sqrt{- 1 (50)}$ as $\sqrt{- 1} \cdot \sqrt{50}$ .

$12 - (\sqrt{- 1} \cdot \sqrt{50}) - \sqrt{49} - \sqrt{- 98}$

Step 1.6

Rewrite $\sqrt{- 1}$ as $i$ .

$12 - (i \cdot \sqrt{50}) - \sqrt{49} - \sqrt{- 98}$

Step 1.7

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 1.7.1

Factor $25$ out of $50$ .

$12 - (i \cdot \sqrt{25 (2)}) - \sqrt{49} - \sqrt{- 98}$

Step 1.7.2

Rewrite $25$ as $5^{2}$ .

$12 - (i \cdot \sqrt{5^{2} \cdot 2}) - \sqrt{49} - \sqrt{- 98}$

Step 1.8

Pull terms out from under the radical.

$12 - (i \cdot (| 5 | \sqrt{2})) - \sqrt{49} - \sqrt{- 98}$

Step 1.9

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$12 - (i \cdot (5 \sqrt{2})) - \sqrt{49} - \sqrt{- 98}$

Step 1.10

Move $5$ to the left of $i$ .

$12 - (5 \cdot i \sqrt{2}) - \sqrt{49} - \sqrt{- 98}$

Step 1.11

Multiply $5$ by $- 1$ .

$12 - 5 (i \sqrt{2}) - \sqrt{49} - \sqrt{- 98}$

Step 1.12

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

$12 - 5 i \sqrt{2} - \sqrt{7^{2}} - \sqrt{- 98}$

Step 1.13

Pull terms out from under the radical.

$12 - 5 i \sqrt{2} - | 7 | - \sqrt{- 98}$

Step 1.14

The absolute value is the distance between a number and zero. The distance between $0$ and $7$ is $7$ .

$12 - 5 i \sqrt{2} - 1 \cdot 7 - \sqrt{- 98}$

Step 1.15

Multiply $- 1$ by $7$ .

$12 - 5 i \sqrt{2} - 7 - \sqrt{- 98}$

Step 1.16

Rewrite $- 98$ as $- 1 (98)$ .

$12 - 5 i \sqrt{2} - 7 - \sqrt{- 1 (98)}$

Step 1.17

Rewrite $\sqrt{- 1 (98)}$ as $\sqrt{- 1} \cdot \sqrt{98}$ .

$12 - 5 i \sqrt{2} - 7 - (\sqrt{- 1} \cdot \sqrt{98})$

Step 1.18

Rewrite $\sqrt{- 1}$ as $i$ .

$12 - 5 i \sqrt{2} - 7 - (i \cdot \sqrt{98})$

Step 1.19

Rewrite $98$ as $7^{2} \cdot 2$ .

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Step 1.19.1

Factor $49$ out of $98$ .

$12 - 5 i \sqrt{2} - 7 - (i \cdot \sqrt{49 (2)})$

Step 1.19.2

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

$12 - 5 i \sqrt{2} - 7 - (i \cdot \sqrt{7^{2} \cdot 2})$

Step 1.20

Pull terms out from under the radical.

$12 - 5 i \sqrt{2} - 7 - (i \cdot (| 7 | \sqrt{2}))$

Step 1.21

The absolute value is the distance between a number and zero. The distance between $0$ and $7$ is $7$ .

$12 - 5 i \sqrt{2} - 7 - (i \cdot (7 \sqrt{2}))$

Step 1.22

Move $7$ to the left of $i$ .

$12 - 5 i \sqrt{2} - 7 - (7 \cdot i \sqrt{2})$

Step 1.23

Multiply $7$ by $- 1$ .

$12 - 5 i \sqrt{2} - 7 - 7 i \sqrt{2}$

Step 2

Subtract $7$ from $12$ .

$- 5 i \sqrt{2} + 5 - 7 i \sqrt{2}$

Step 3

Subtract $7 i \sqrt{2}$ from $- 5 i \sqrt{2}$ .

$- 12 i \sqrt{2} + 5$

Step 4

Reorder $- 12 i \sqrt{2}$ and $5$ .

$5 - 12 i \sqrt{2}$