Step by step
The question
Question: work out 25^(1/2).
25^(1/2)
A fraction power has two jobs.
The bottom number, 2, says which root: the square root.
The top number, 1, says which power.
For the square root, the small 2 is not written.
a^(m/n) = (n√a)m
Careful!
The power is not times.
25 times 1/2 is a different number.
Careful: not 25^(1/2) = 25 × 12 ✗
1 Write it as a root
The bottom is 2, so it is the square root of 25.
The top is 1: power 1 changes nothing.
= √25
√25 is 5, because 5 × 5 is 25.
5 × 5 = 25
So 25^(1/2) = 5.
= 5
2 Check
Let's check: 5 times itself 2 times.
We get 25.
So the answer is right!
5 × 5 = 25
Let's look back.
First: write it as a root.
Last: check.
Answer
= 5