Step by step
The question
Question: solve √(x + 3) = 4.
√x + 3 = 4
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 + 3)2 = 42
The square removes the square root.
4 squared is 16.
x + 3 = 16
2 Remove the + 3
We want x by itself.
The + 3 is in the way.
To remove + 3, we take away 3.
We do it on both sides, so they stay equal.
x + 3 − 3 = 16 − 3
+ 3 and − 3 make zero.
Cross them out.
16 − 3 = 13.
16 − 3 = 13
So x = 13!
x = 13
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 = 13 in the question.
The left side is 4.
x = 13: √13 + 3 = √16 = 4
The right side is 4.
The same!
x = 13 works.
right side: 4 ✓
Let's look back.
First: square both sides.
Then: remove the + 3.
Last: check.
Answer
x = 13