Simplify the Radical Expression square root of 49- square root of -200+ square root of 81+ square root of -32

$\sqrt{49} - \sqrt{- 200} + \sqrt{81} + \sqrt{- 32}$

Simplify each term.

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

$\sqrt{7^{2}} - \sqrt{- 200} + \sqrt{81} + \sqrt{- 32}$

Pull terms out from under the radical.

$| 7 | - \sqrt{- 200} + \sqrt{81} + \sqrt{- 32}$

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

$7 - \sqrt{- 200} + \sqrt{81} + \sqrt{- 32}$

Rewrite $- 200$ as $- 1 (200)$ .

$7 - \sqrt{- 1 (200)} + \sqrt{81} + \sqrt{- 32}$

Rewrite $\sqrt{- 1 (200)}$ as $\sqrt{- 1} \cdot \sqrt{200}$ .

$7 - (\sqrt{- 1} \cdot \sqrt{200}) + \sqrt{81} + \sqrt{- 32}$

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

$7 - (i \cdot \sqrt{200}) + \sqrt{81} + \sqrt{- 32}$

Rewrite $200$ as $10^{2} \cdot 2$ .

Factor $100$ out of $200$ .

$7 - (i \cdot \sqrt{100 (2)}) + \sqrt{81} + \sqrt{- 32}$

Rewrite $100$ as $10^{2}$ .

$7 - (i \cdot \sqrt{10^{2} \cdot 2}) + \sqrt{81} + \sqrt{- 32}$

Pull terms out from under the radical.

$7 - (i \cdot (| 10 | \sqrt{2})) + \sqrt{81} + \sqrt{- 32}$

The absolute value is the distance between a number and zero. The distance between $0$ and $10$ is $10$ .

$7 - (i \cdot (10 \sqrt{2})) + \sqrt{81} + \sqrt{- 32}$

Move $10$ to the left of $i$ .

$7 - (10 \cdot i \sqrt{2}) + \sqrt{81} + \sqrt{- 32}$

Multiply $10$ by $- 1$ .

$7 - 10 (i \sqrt{2}) + \sqrt{81} + \sqrt{- 32}$

Rewrite $81$ as $9^{2}$ .

$7 - 10 i \sqrt{2} + \sqrt{9^{2}} + \sqrt{- 32}$

Pull terms out from under the radical.

$7 - 10 i \sqrt{2} + | 9 | + \sqrt{- 32}$

The absolute value is the distance between a number and zero. The distance between $0$ and $9$ is $9$ .

$7 - 10 i \sqrt{2} + 9 + \sqrt{- 32}$

Rewrite $- 32$ as $- 1 (32)$ .

$7 - 10 i \sqrt{2} + 9 + \sqrt{- 1 (32)}$

Rewrite $\sqrt{- 1 (32)}$ as $\sqrt{- 1} \cdot \sqrt{32}$ .

$7 - 10 i \sqrt{2} + 9 + \sqrt{- 1} \cdot \sqrt{32}$

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

$7 - 10 i \sqrt{2} + 9 + i \cdot \sqrt{32}$

Rewrite $32$ as $4^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$7 - 10 i \sqrt{2} + 9 + i \cdot \sqrt{16 (2)}$

Rewrite $16$ as $4^{2}$ .

$7 - 10 i \sqrt{2} + 9 + i \cdot \sqrt{4^{2} \cdot 2}$

Pull terms out from under the radical.

$7 - 10 i \sqrt{2} + 9 + i \cdot (| 4 | \sqrt{2})$

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$7 - 10 i \sqrt{2} + 9 + i \cdot (4 \sqrt{2})$

Move $4$ to the left of $i$ .

$7 - 10 i \sqrt{2} + 9 + 4 i \sqrt{2}$

Add $7$ and $9$ .

$- 10 i \sqrt{2} + 16 + 4 i \sqrt{2}$

Add $- 10 i \sqrt{2}$ and $4 i \sqrt{2}$ .

$- 6 i \sqrt{2} + 16$

Reorder $- 6 i \sqrt{2}$ and $16$ .

$16 - 6 i \sqrt{2}$

Simplify the Radical Expression square root of 49- square root of -200+ square root of 81+ square root of -32

Related Questions

Support LCMGCF.com by disabling your adblocker.