Algebra Examples

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

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

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

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

Step 1.4

Multiply $- 1$ by $5$ .

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

Step 1.5

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

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

Step 1.6

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

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

Step 1.7

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

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

Step 1.8

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

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

Step 1.9

Pull terms out from under the radical.

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

Step 1.10

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

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

Step 1.11

Multiply $- 1$ by $10$ .

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

Step 1.12

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

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

Step 1.13

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

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

Step 1.14

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

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

Step 1.15

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

Tap for more steps...

Step 1.15.1

Factor $9$ out of $63$ .

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

Step 1.15.2

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

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

Step 1.16

Pull terms out from under the radical.

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

Step 1.17

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

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

Step 1.18

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

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

Step 1.19

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 $- 15$ .

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