Step by step
The question
Question: simplify √(50y²).
√50y2
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 50 is 25: 50 is 25 times 2.
A square of letters has an even power.
y² is y squared, because y times y is y²: the powers add.
50 = 25 × 2
y2 = y2, y² = (y)²
We write the squares first, then what is left.
= √25y2 × 2
2 Take the square roots
Rule: a root over a times can be split into two roots.
√(a × b) = √a × √b
So we get two roots.
= √25y2 × √2
√25 is 5.
The root halves each even power: √y² is y.
√25 = 5, √y² = y
So √(50y²) = 5y√2.
= 5y√2
3 Check
Let's check: we square the answer.
We must get 50y² back.
A root times itself is what is inside.
Squaring doubles each power.
Check: (5y√2)2 = (5y)2 × 2 = 25y2 × 2
= 50y2
We get 50y².
So 5y√2 is right!
Let's look back.
First: find the squares.
Then: take the square roots.
Last: check.
Answer
= 5y√2