Step by step
The question
Question: work out √5 × √20.
√5 × √20
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 5 times 20.
= √5 × 20
Careful!
This works for times, not for plus.
√9 + √16 is 3 + 4 = 7, but √25 is 5.
Careful: not √5 + √20 = √25 ✗
only for ×: √9 + √16 = 7, √25 = 5
5 times 20 is 100.
= √100
2 Simplify the root
100 is a square number: 10 times 10 is 100.
So √100 is 10.
10 × 10 = 100
So we get 10.
So √5 × √20 = 10.
= 10
3 Check
Let's check with a calculator.
The start is about 10.00.
Start: √5 × √20 ≈ 10.00
The answer is about 10.00 too.
So it is right!
Answer: 10 ≈ 10.00
Let's look back.
First: multiply.
Then: simplify the root.
Last: check.
Answer
= 10