Step by step
The question
Question: simplify 8√18/2√2.
8√182√2
1 One root
Rule: a root over a root is the root of the fraction.
√a√b = √ab
The numbers outside make their own fraction.
The roots go under one root.
= 82 × √182
18 divided by 2 is 9.
8/2 is 4.
18 ÷ 2 = 9, 8 ÷ 2 = 4
So we get 4√9.
= 4√9
2 Simplify the root
9 is a square number: 3 times 3 is 9.
So √9 is 3.
3 × 3 = 9
4 times 3 is 12.
So the answer is 12.
= 12
Careful!
18 divided by 2 is 9.
But the answer is the ROOT of 9.
Don't drop the root.
Careful: not √18√2 = 9 ✗
3 Check
Let's check with a calculator.
The start is about 12.00.
Start: 8√182√2 ≈ 12.00
The answer is about 12.00 too.
So it is right!
Answer: 12 ≈ 12.00
Let's look back.
First: one root.
Then: simplify the root.
Last: check.
Answer
= 12