Step by step
The question
Question: solve √(x − 4) = 0.
√x − 4 = 0
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 − 4)2 = 02
The square removes the square root.
0 squared is 0.
x − 4 = 0
2 Remove the − 4
We want x by itself.
The − 4 is in the way.
To remove − 4, we add 4.
We do it on both sides, so they stay equal.
x − 4 + 4 = 0 + 4
− 4 and + 4 make zero.
Cross them out.
0 + 4 = 4.
0 + 4 = 4
So x = 4!
x = 4
3 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 = 4 in the question.
The left side is 0.
x = 4: √4 − 4 = √0 = 0
The right side is 0.
The same!
x = 4 works.
right side: 0 ✓
Let's look back.
First: square both sides.
Then: remove the − 4.
Last: check.
Answer
x = 4