Step by step
The question
Question: work out √2 × √8.
√2 × √8
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 8.
= √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.
= √16
2 Simplify the root
16 is a square number: 4 times 4 is 16.
So √16 is 4.
4 × 4 = 16
So we get 4.
So √2 × √8 = 4.
= 4
3 Check
Let's check with a calculator.
The start is about 4.00.
Start: √2 × √8 ≈ 4.00
The answer is about 4.00 too.
So it is right!
Answer: 4 ≈ 4.00
Let's look back.
First: multiply.
Then: simplify the root.
Last: check.
Answer
= 4