Step by step
The question
Question: work out √3 × √12.
√3 × √12
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 3 times 12.
= √3 × 12
Careful!
This works for times, not for plus.
√9 + √16 is 3 + 4 = 7, but √25 is 5.
Careful: not √3 + √12 = √15 ✗
only for ×: √9 + √16 = 7, √25 = 5
3 times 12 is 36.
= √36
2 Simplify the root
36 is a square number: 6 times 6 is 36.
So √36 is 6.
6 × 6 = 36
So we get 6.
So √3 × √12 = 6.
= 6
3 Check
Let's check with a calculator.
The start is about 6.00.
Start: √3 × √12 ≈ 6.00
The answer is about 6.00 too.
So it is right!
Answer: 6 ≈ 6.00
Let's look back.
First: multiply.
Then: simplify the root.
Last: check.
Answer
= 6