Step by step
The question
Question: simplify √(9x²).
√9x2
Like the books, we take every letter as a number that is not negative.
letters are not negative here
1 Find the squares
The biggest square in 9 is 9: 9 is 9 times 1.
A square of letters has an even power.
x² is x squared, because x times x is x²: the powers add.
9 = 9 × 1
x2 = x2, x² = (x)²
Everything under the root is a square.
= √9x2
2 Take the square roots
√9 is 3.
The root halves each even power: √x² is x.
√9 = 3, √x² = x
So √(9x²) = 3x.
= 3x
3 Check
Let's check: we square the answer.
We must get 9x² back.
Squaring doubles each power.
Check: (3x)2 = 9x2
We get 9x².
So 3x is right!
Let's look back.
First: find the squares.
Then: take the square roots.
Last: check.
Answer
= 3x