Step by step
The question
Question: work out 5√2 × √3.
5√2 × √3
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.
= 5 × 1 × √2 × √3
5 times 1 is 5.
5 × 1 = 5
So it is 5 times the root of 2 times 3.
= 5√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.
= 5√6
2 Simplify the root
No square number goes into 6.
So 5√6 is as simple as it gets.
3 Check
Let's check with a calculator.
The start is about 12.25.
Start: 5√2 × √3 ≈ 12.25
The answer is about 12.25 too.
So it is right!
Answer: 5√6 ≈ 12.25
Let's look back.
First: multiply.
Then: simplify the root.
Last: check.
Answer
= 5√6