Help... please and thank you.

Question

I get really confused with square rooting and my teacher said the answer I got was wrong.

Sqrt (x^10)

Answer 1

√(x¹⁰) = (x¹⁰)^½ = x^(10)(½) = x⁵

Answer 2

√x¹⁰ = x⁵

 

because √x¹⁰ = √x⁵x⁵

 

In general, if the exponent of the coefficient is even, like 10, you can bring it out of the radical with an exponent equal

 

to half of what is was like:

 

√x⁶ =x³

 

If the exponent of the coefficient is odd, like 9, subtract one (9-1 = 8) and take half (half of 8 = 4). That will come out of

 

the radical. However, there will be a variablle with an exponent of 1 remaining in the radical like this.

 

√x⁹ = x⁴√x

 

because √x⁹ = √x⁴x⁴x

 

Hope this helps