How do you simplify sqrt(-9)√−9?

2 Answers
Aviv S.
Mar 25, 2018

The expression is equal to 3i3i.

Explanation:

Remember these two radical rules:

sqrt(color(red)acolor(blue)b)=sqrtcolor(red)a*sqrtcolor(blue)b√ab=√a⋅√b

sqrt(color(red)a^2)=color(red)a√a2=a

And also the definition of the imaginary number:

sqrt(-1)=i√−1=i

Here are these properties applied to our expression.

color(white)=sqrt(-9)=√−9

=sqrt(-3*3)=√−3⋅3

=sqrt(-1*3*3)=√−1⋅3⋅3

=sqrt(-1*3^2)=√−1⋅32

=sqrt(-1)*sqrt(3^2)=√−1⋅√32

=sqrt(-1)*3=√−1⋅3

=i*3=i⋅3

=3i=3i

This is the result. Hope this helped!

Meave60
Mar 25, 2018

sqrt(-9)=3i√−9=3i

Explanation:

Given:

sqrt(-9)√−9

Prime factorize the radicand.

sqrt(3^2xx-1)√32×−1

Apply rule: sqrt(a^2)=a√a2=a, and sqrt(-1)=i√−1=i.

Simplify.

3i3i

Related questions
See all questions in Simplification of Radical Expressions
Impact of this question
2758 views around the world
You can reuse this answer
Creative Commons License