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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?
10 and -10
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 square roots of 100.
a^2= 100
Because n=2 is even and b=100 is positive, there are two square roots of 100.
We found the positive square root of 100, which also gives us the negative root. Positive Root:& a_1= 10 Negative Root:& a_2=-10