Simplify 7i square root of -75

$7 i \sqrt{- 75}$

Rewrite $- 75$ as $- 1 (75)$ .

$7 i \sqrt{- 1 (75)}$

Rewrite $\sqrt{- 1 (75)}$ as $\sqrt{- 1} \cdot \sqrt{75}$ .

$7 i (\sqrt{- 1} \cdot \sqrt{75})$

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

$7 i (i \cdot \sqrt{75})$

Rewrite $75$ as $5^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$7 i (i \cdot \sqrt{25 (3)})$

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

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

Pull terms out from under the radical.

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

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

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

Multiply $7 i (5 i \sqrt{3})$ .

Multiply $5$ by $7$ .

$35 i (i \sqrt{3})$

Raise $i$ to the power of $1$ .

$35 (i^{1} i) \sqrt{3}$

Raise $i$ to the power of $1$ .

$35 (i^{1} i^{1}) \sqrt{3}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$35 i^{1 + 1} \sqrt{3}$

Add $1$ and $1$ .

$35 i^{2} \sqrt{3}$

Rewrite $i^{2}$ as $- 1$ .

$35 \cdot - 1 \sqrt{3}$

Multiply $35$ by $- 1$ .

$- 35 \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$- 35 \sqrt{3}$

Decimal Form:

$- 60.62177826 \dots$