Step by step
The question
Question: simplify √(16x³y²).
Like the books, we take every letter as a number that is not negative.
1 Find the squares
The biggest square in 16 is 16: 16 is 16 times 1.
A square of letters has an even power.
x³ is x² times x.
x² is x squared, because x times x is x²: the powers add.
y² is y squared, because y times y is y²: the powers add.
We write the squares first, then what is left.
2 Take the square roots
Rule: a root over a times can be split into two roots.
So we get two roots.
√16 is 4.
The root halves each even power: √x² is x, √y² is y.
So √(16x³y²) = 4xy√x.
3 Check
Let's check: we square the answer.
We must get 16x³y² back.
A root times itself is what is inside.
Squaring doubles each power.
We get 16x³y².
So 4xy√x is right!
Let's look back.
First: find the squares.
Then: take the square roots.
Last: check.