Step by step
The question
Question: work out √2 × √18.
√2 × √18
1 Multiply
Rule: two roots times each other make one root of the two numbers times each other.
√a × √b = √(a × b)
So it is the root of 2 times 18.
= √2 × 18
Careful!
This works for times, not for plus.
√9 + √16 is 3 + 4 = 7, but √25 is 5.
Careful: not √2 + √18 = √20 ✗
only for ×: √9 + √16 = 7, √25 = 5
2 times 18 is 36.
= √36
2 Simplify the root
36 is a square number: 6 times 6 is 36.
So √36 is 6.
6 × 6 = 36
So we get 6.
So √2 × √18 = 6.
= 6
3 Check
Let's check with a calculator.
The start is about 6.00.
Start: √2 × √18 ≈ 6.00
The answer is about 6.00 too.
So it is right!
Answer: 6 ≈ 6.00
Let's look back.
First: multiply.
Then: simplify the root.
Last: check.
Answer
= 6