Simplify the Radical Expression - square root of 25+ square root of -7- square root of 100- square root of -63

$- \sqrt{25} + \sqrt{- 7} - \sqrt{100} - \sqrt{- 63}$

Step 1

Simplify each term.

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

$- \sqrt{5^{2}} + \sqrt{- 7} - \sqrt{100} - \sqrt{- 63}$

Pull terms out from under the radical.

$- | 5 | + \sqrt{- 7} - \sqrt{100} - \sqrt{- 63}$

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

$- 1 \cdot 5 + \sqrt{- 7} - \sqrt{100} - \sqrt{- 63}$

Multiply $- 1$ by $5$ .

$- 5 + \sqrt{- 7} - \sqrt{100} - \sqrt{- 63}$

Rewrite $- 7$ as $- 1 (7)$ .

$- 5 + \sqrt{- 1 (7)} - \sqrt{100} - \sqrt{- 63}$

Rewrite $\sqrt{- 1 (7)}$ as $\sqrt{- 1} \cdot \sqrt{7}$ .

$- 5 + \sqrt{- 1} \cdot \sqrt{7} - \sqrt{100} - \sqrt{- 63}$

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

$- 5 + i \cdot \sqrt{7} - \sqrt{100} - \sqrt{- 63}$

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

$- 5 + i \sqrt{7} - \sqrt{10^{2}} - \sqrt{- 63}$

Pull terms out from under the radical.

$- 5 + i \sqrt{7} - | 10 | - \sqrt{- 63}$

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

$- 5 + i \sqrt{7} - 1 \cdot 10 - \sqrt{- 63}$

Multiply $- 1$ by $10$ .

$- 5 + i \sqrt{7} - 10 - \sqrt{- 63}$

Rewrite $- 63$ as $- 1 (63)$ .

$- 5 + i \sqrt{7} - 10 - \sqrt{- 1 (63)}$

Rewrite $\sqrt{- 1 (63)}$ as $\sqrt{- 1} \cdot \sqrt{63}$ .

$- 5 + i \sqrt{7} - 10 - (\sqrt{- 1} \cdot \sqrt{63})$

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

$- 5 + i \sqrt{7} - 10 - (i \cdot \sqrt{63})$

Rewrite $63$ as $3^{2} \cdot 7$ .

Factor $9$ out of $63$ .

$- 5 + i \sqrt{7} - 10 - (i \cdot \sqrt{9 (7)})$

Rewrite $9$ as $3^{2}$ .

$- 5 + i \sqrt{7} - 10 - (i \cdot \sqrt{3^{2} \cdot 7})$

Pull terms out from under the radical.

$- 5 + i \sqrt{7} - 10 - (i \cdot (| 3 | \sqrt{7}))$

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$- 5 + i \sqrt{7} - 10 - (i \cdot (3 \sqrt{7}))$

Move $3$ to the left of $i$ .

$- 5 + i \sqrt{7} - 10 - (3 \cdot i \sqrt{7})$

Multiply $3$ by $- 1$ .

$- 5 + i \sqrt{7} - 10 - 3 i \sqrt{7}$

Step 2

Subtract $10$ from $- 5$ .

$i \sqrt{7} - 15 - 3 i \sqrt{7}$

Step 3

Subtract $3 i \sqrt{7}$ from $i \sqrt{7}$ .

$- 2 i \sqrt{7} - 15$

Step 4

Reorder $- 2 i \sqrt{7}$ and $- 15$ .

$- 15 - 2 i \sqrt{7}$

Simplify the Radical Expression - square root of 25+ square root of -7- square root of 100- square root of -63

Related Questions

Support LCMGCF.com by disabling your adblocker.