Step by step
The question
Question: solve √(x + 5) = 6.
√x + 5 = 6
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 + 5)2 = 62
The square removes the square root.
6 squared is 36.
x + 5 = 36
2 Remove the + 5
We want x by itself.
The + 5 is in the way.
To remove + 5, we take away 5.
We do it on both sides, so they stay equal.
x + 5 − 5 = 36 − 5
+ 5 and − 5 make zero.
Cross them out.
36 − 5 = 31.
36 − 5 = 31
So x = 31!
x = 31
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 = 31 in the question.
The left side is 6.
x = 31: √31 + 5 = √36 = 6
The right side is 6.
The same!
x = 31 works.
right side: 6 ✓
Let's look back.
First: square both sides.
Then: remove the + 5.
Last: check.
Answer
x = 31