Simplify the Radical Expression square root of 144+ square root of -98- square root of 121+ square root of -2

$\sqrt{144} + \sqrt{- 98} - \sqrt{121} + \sqrt{- 2}$

Step 1

Simplify each term.

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

$\sqrt{12^{2}} + \sqrt{- 98} - \sqrt{121} + \sqrt{- 2}$

Pull terms out from under the radical.

$| 12 | + \sqrt{- 98} - \sqrt{121} + \sqrt{- 2}$

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

$12 + \sqrt{- 98} - \sqrt{121} + \sqrt{- 2}$

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

$12 + \sqrt{- 1 (98)} - \sqrt{121} + \sqrt{- 2}$

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

$12 + \sqrt{- 1} \cdot \sqrt{98} - \sqrt{121} + \sqrt{- 2}$

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

$12 + i \cdot \sqrt{98} - \sqrt{121} + \sqrt{- 2}$

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

Factor $49$ out of $98$ .

$12 + i \cdot \sqrt{49 (2)} - \sqrt{121} + \sqrt{- 2}$

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

$12 + i \cdot \sqrt{7^{2} \cdot 2} - \sqrt{121} + \sqrt{- 2}$

Pull terms out from under the radical.

$12 + i \cdot (| 7 | \sqrt{2}) - \sqrt{121} + \sqrt{- 2}$

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

$12 + i \cdot (7 \sqrt{2}) - \sqrt{121} + \sqrt{- 2}$

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

$12 + 7 \cdot i \sqrt{2} - \sqrt{121} + \sqrt{- 2}$

Rewrite $121$ as $11^{2}$ .

$12 + 7 i \sqrt{2} - \sqrt{11^{2}} + \sqrt{- 2}$

Pull terms out from under the radical.

$12 + 7 i \sqrt{2} - | 11 | + \sqrt{- 2}$

The absolute value is the distance between a number and zero. The distance between $0$ and $11$ is $11$ .

$12 + 7 i \sqrt{2} - 1 \cdot 11 + \sqrt{- 2}$

Multiply $- 1$ by $11$ .

$12 + 7 i \sqrt{2} - 11 + \sqrt{- 2}$

Rewrite $- 2$ as $- 1 (2)$ .

$12 + 7 i \sqrt{2} - 11 + \sqrt{- 1 (2)}$

Rewrite $\sqrt{- 1 (2)}$ as $\sqrt{- 1} \cdot \sqrt{2}$ .

$12 + 7 i \sqrt{2} - 11 + \sqrt{- 1} \cdot \sqrt{2}$

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

$12 + 7 i \sqrt{2} - 11 + i \sqrt{2}$

Step 2

Subtract $11$ from $12$ .

$7 i \sqrt{2} + 1 + i \sqrt{2}$

Step 3

Add $7 i \sqrt{2}$ and $i \sqrt{2}$ .

$8 i \sqrt{2} + 1$

Step 4

Reorder $8 i \sqrt{2}$ and $1$ .

$1 + 8 i \sqrt{2}$

Simplify the Radical Expression square root of 144+ square root of -98- square root of 121+ square root of -2

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