Step by step
The question
Question: solve √2x = 4.
√2x = 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.
(√2x)2 = 42
The square removes the square root.
4 squared is 16.
2x = 16
2 Remove the 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just x is left.
16 divided by 2 is 8.
162 = 8
So x = 8!
x = 8
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 = 8 in the question.
The left side is 4.
x = 8: √2(8) = √16 = 4
The right side is 4.
The same!
x = 8 works.
right side: 4 ✓
Let's look back.
First: square both sides.
Then: remove the 2.
Last: check.
Answer
x = 8