Step by step
The question
Question: work out 3√2 × 4√8.
3√2 × 4√8
1 Multiply
Rule: two roots times each other make one root of the two numbers times each other.
√a × √b = √(a × b)
Times can go in any order.
So we put the numbers outside together, and the roots together.
= 3 × 4 × √2 × √8
3 times 4 is 12.
3 × 4 = 12
So it is 12 times the root of 2 times 8.
= 12√2 × 8
Careful!
This works for times, not for plus.
√9 + √16 is 3 + 4 = 7, but √25 is 5.
Careful: not √2 + √8 = √10 ✗
only for ×: √9 + √16 = 7, √25 = 5
2 times 8 is 16.
= 12√16
2 Simplify the root
16 is a square number: 4 times 4 is 16.
So √16 is 4.
4 × 4 = 16
12 times 4 is 48.
So 3√2 × 4√8 = 48.
= 48
3 Check
Let's check with a calculator.
The start is about 48.00.
Start: 3√2 × 4√8 ≈ 48.00
The answer is about 48.00 too.
So it is right!
Answer: 48 ≈ 48.00
Let's look back.
First: multiply.
Then: simplify the root.
Last: check.
Answer
= 48