Step by step
The question
Question: solve √x = 5.
√x = 5
1 Square both sides
Squaring removes the square root.
The square root of 9 is 3, and 3 squared is 9 again.
(√9)² = 9
We square both sides, so they stay equal.
(√x)2 = 52
The square removes the square root.
5 squared is 25.
x = 25
So x = 25!
2 Check
Careful!
Squaring can make an answer that does not work.
Why?
Minus 2 squared is 4, and 2 squared is 4 too.
Squaring hides a minus sign.
So we check every answer in the question.
Careful: squaring can make a false answer
(−2)² = 4 and 2² = 4
Let's check x = 25 in the question.
The left side is 5.
x = 25: √25 = 5
The right side is 5.
The same!
x = 25 works.
right side: 5 ✓
Let's look back.
First: square both sides.
Last: check.
Answer
x = 25