Step by step
The question
Question: work out 3√7 × 2√7.
3√7 × 2√7
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 × 2 × √7 × √7
3 times 2 is 6.
3 × 2 = 6
So it is 6 times the root of 7 times 7.
= 6√7 × 7
Careful!
This works for times, not for plus.
√9 + √16 is 3 + 4 = 7, but √25 is 5.
Careful: not √7 + √7 = √14 ✗
only for ×: √9 + √16 = 7, √25 = 5
7 times 7 is 49.
= 6√49
2 Simplify the root
49 is a square number: 7 times 7 is 49.
So √49 is 7.
7 × 7 = 49
6 times 7 is 42.
So 3√7 × 2√7 = 42.
= 42
3 Check
Let's check with a calculator.
The start is about 42.00.
Start: 3√7 × 2√7 ≈ 42.00
The answer is about 42.00 too.
So it is right!
Answer: 42 ≈ 42.00
Let's look back.
First: multiply.
Then: simplify the root.
Last: check.
Answer
= 42