Simplify square root of 25- square root of -25- square root of 36- square root of -4

$\sqrt{25} - \sqrt{- 25} - \sqrt{36} - \sqrt{- 4}$

Step 1

Simplify each term.

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

$\sqrt{5^{2}} - \sqrt{- 25} - \sqrt{36} - \sqrt{- 4}$

Pull terms out from under the radical, assuming positive real numbers.

$5 - \sqrt{- 25} - \sqrt{36} - \sqrt{- 4}$

Rewrite $- 25$ as $- 1 (25)$ .

$5 - \sqrt{- 1 (25)} - \sqrt{36} - \sqrt{- 4}$

Rewrite $\sqrt{- 1 (25)}$ as $\sqrt{- 1} \cdot \sqrt{25}$ .

$5 - (\sqrt{- 1} \cdot \sqrt{25}) - \sqrt{36} - \sqrt{- 4}$

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

$5 - (i \cdot \sqrt{25}) - \sqrt{36} - \sqrt{- 4}$

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

$5 - (i \cdot \sqrt{5^{2}}) - \sqrt{36} - \sqrt{- 4}$

Pull terms out from under the radical, assuming positive real numbers.

$5 - (i \cdot 5) - \sqrt{36} - \sqrt{- 4}$

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

$5 - (5 \cdot i) - \sqrt{36} - \sqrt{- 4}$

Multiply $5$ by $- 1$ .

$5 - 5 i - \sqrt{36} - \sqrt{- 4}$

Rewrite $36$ as $6^{2}$ .

$5 - 5 i - \sqrt{6^{2}} - \sqrt{- 4}$

Pull terms out from under the radical, assuming positive real numbers.

$5 - 5 i - 1 \cdot 6 - \sqrt{- 4}$

Multiply $- 1$ by $6$ .

$5 - 5 i - 6 - \sqrt{- 4}$

Rewrite $- 4$ as $- 1 (4)$ .

$5 - 5 i - 6 - \sqrt{- 1 (4)}$

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$5 - 5 i - 6 - (\sqrt{- 1} \cdot \sqrt{4})$

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

$5 - 5 i - 6 - (i \cdot \sqrt{4})$

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

$5 - 5 i - 6 - (i \cdot \sqrt{2^{2}})$

Pull terms out from under the radical, assuming positive real numbers.

$5 - 5 i - 6 - (i \cdot 2)$

Move $2$ to the left of $i$ .

$5 - 5 i - 6 - (2 \cdot i)$

Multiply $2$ by $- 1$ .

$5 - 5 i - 6 - 2 i$

Step 2

Simplify by adding terms.

Subtract $6$ from $5$ .

$- 1 - 5 i - 2 i$

Subtract $2 i$ from $- 5 i$ .

$- 1 - 7 i$

Simplify square root of 25- square root of -25- square root of 36- square root of -4

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