Step by step
The question
Question: work out √2 × √3.
√2 × √3
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 3.
= √2 × 3
Careful!
This works for times, not for plus.
√9 + √16 is 3 + 4 = 7, but √25 is 5.
Careful: not √2 + √3 = √5 ✗
only for ×: √9 + √16 = 7, √25 = 5
2 times 3 is 6.
= √6
2 Simplify the root
No square number goes into 6.
So √6 is as simple as it gets.
3 Check
Let's check with a calculator.
The start is about 2.45.
Start: √2 × √3 ≈ 2.45
The answer is about 2.45 too.
So it is right!
Answer: √6 ≈ 2.45
Let's look back.
First: multiply.
Then: simplify the root.
Last: check.
Answer
= √6