Write in Standard Form square root of -64- square root of -25

$\sqrt{- 64} - \sqrt{- 25}$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Simplify each term.

Rewrite $- 64$ as $- 1 (64)$ .

$\sqrt{- 1 (64)} - \sqrt{- 25}$

Rewrite $\sqrt{- 1 (64)}$ as $\sqrt{- 1} \cdot \sqrt{64}$ .

$\sqrt{- 1} \cdot \sqrt{64} - \sqrt{- 25}$

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

$i \cdot \sqrt{64} - \sqrt{- 25}$

Rewrite $64$ as $8^{2}$ .

$i \cdot \sqrt{8^{2}} - \sqrt{- 25}$

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

$i \cdot 8 - \sqrt{- 25}$

Move $8$ to the left of $i$ .

$8 \cdot i - \sqrt{- 25}$

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

$8 i - \sqrt{- 1 (25)}$

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

$8 i - (\sqrt{- 1} \cdot \sqrt{25})$

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

$8 i - (i \cdot \sqrt{25})$

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

$8 i - (i \cdot \sqrt{5^{2}})$

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

$8 i - (i \cdot 5)$

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

$8 i - (5 \cdot i)$

Multiply $5$ by $- 1$ .

$8 i - 5 i$

Step 3

Subtract $5 i$ from $8 i$ .

$3 i$