Step by step
The question
Question: solve 3√(x − 1) = 6.
1 Get the root alone
3√(x − 1) means 3 times the square root.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just the square root is left.
6 divided by 3 is 2.
2 Square both sides
Squaring removes the square root.
The square root of 9 is 3, and 3 squared is 9 again.
We square both sides, so they stay equal.
The square removes the square root.
2 squared is 4.
3 Remove the − 1
We want x by itself.
The − 1 is in the way.
To remove − 1, we add 1.
We do it on both sides, so they stay equal.
− 1 and + 1 make zero.
Cross them out.
4 + 1 = 5.
So x = 5!
4 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.
Let's check x = 5 in the question.
The left side is 6.
The right side is 6.
The same!
x = 5 works.
Let's look back.
First: get the root alone.
Then: square both sides.
Then: remove the − 1.
Last: check.