Step by step
The question
Question: work out √6 × √10.
√6 × √10
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 6 times 10.
= √6 × 10
Careful!
This works for times, not for plus.
√9 + √16 is 3 + 4 = 7, but √25 is 5.
Careful: not √6 + √10 = √16 ✗
only for ×: √9 + √16 = 7, √25 = 5
6 times 10 is 60.
= √60
2 Simplify the root
Now we make √60 simpler, like in the lesson on square roots.
25 does not go into 60.
16 does not go into 60.
9 does not go into 60.
The biggest square that goes into 60 is 4: 60 divided by 4 is 15.
Square numbers: 4, 9, 16, 25
60 ÷ 4 = 15 ✓
So √60 is √4 times √15.
= √4 × √15
√4 is 2, because 2 times 2 is 4.
2 × 2 = 4
So we get 2√15.
So √6 × √10 = 2√15.
= 2√15
3 Check
Let's check with a calculator.
The start is about 7.75.
Start: √6 × √10 ≈ 7.75
The answer is about 7.75 too.
So it is right!
Answer: 2√15 ≈ 7.75
Let's look back.
First: multiply.
Then: simplify the root.
Last: check.
Answer
= 2√15