If a^n=b, where a and b are real numbers and n is a positive integer, then a is an n^\text{th} root of b. How many real n^\text{th} roots are there for positive b if n is even?
± 19/5
Practice makes perfect
If a^n= b, where a and b are real numbers and n is a positive integer, then a is an {\color{#009600}{n}}^\text{th} root of b. In our case, we want to find all the real 2^\text{nd} roots of 36125.
a^2= 361/25
Because n=2 is even and b= 36125 is positive, there are two 2^\text{nd} roots of 36125.
Positive Root:& a_1= sqrt(361/25)
Negative Root:& a_2=-sqrt(361/25)
Let's start with the positive root. Since the 2^\text{nd} roots are squares, we will first write b= 36125 as a power with an exponent of 2.
