How do you simplify $\sqrt{- 9}$ $sqrt(-9)$ ?

Question

How do you simplify $\sqrt{- 9}$ $sqrt(-9)$ ?

2 Answers

Impact of this question

2759 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-25T23:37:25

The expression is equal to $3 i$ $3i$ .

Explanation:

Remember these two radical rules:

$\sqrt{a b} = \sqrt{a} \cdot \sqrt{b}$ $sqrt(color(red)acolor(blue)b)=sqrtcolor(red)a*sqrtcolor(blue)b$

$\sqrt{a^{2}} = a$ $sqrt(color(red)a^2)=color(red)a$

And also the definition of the imaginary number:

$\sqrt{- 1} = i$ $sqrt(-1)=i$

Here are these properties applied to our expression.

$= \sqrt{- 9}$ $color(white)=sqrt(-9)$

$= \sqrt{- 3 \cdot 3}$ $=sqrt(-3*3)$

$= \sqrt{- 1 \cdot 3 \cdot 3}$ $=sqrt(-1*3*3)$

$= \sqrt{- 1 \cdot 3^{2}}$ $=sqrt(-1*3^2)$

$= \sqrt{- 1} \cdot \sqrt{3^{2}}$ $=sqrt(-1)*sqrt(3^2)$

$= \sqrt{- 1} \cdot 3$ $=sqrt(-1)*3$

$= i \cdot 3$ $=i*3$

$= 3 i$ $=3i$

This is the result. Hope this helped!

Answer 2 · 2018-03-25T23:43:22

$\sqrt{- 9} = 3 i$ $sqrt(-9)=3i$

Explanation:

Given:

$\sqrt{- 9}$ $sqrt(-9)$

Prime factorize the radicand.

$\sqrt{3^{2} \times - 1}$ $sqrt(3^2xx-1)$

Apply rule: $\sqrt{a^{2}} = a$ $sqrt(a^2)=a$ , and $\sqrt{- 1} = i$ $sqrt(-1)=i$ .

Simplify.

$3 i$ $3i$

Science

Math

Humanities

... and beyond

How do you simplify $\sqrt{- 9}$ $sqrt(-9)$ ?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you simplify √−9sqrt(-9)?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

How do you simplify $\sqrt{- 9}$ $sqrt(-9)$ ?