Step by step
The question
Question: work out √3 × √15.
√3 × √15
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 15.
= √3 × 15
Careful!
This works for times, not for plus.
√9 + √16 is 3 + 4 = 7, but √25 is 5.
Careful: not √3 + √15 = √18 ✗
only for ×: √9 + √16 = 7, √25 = 5
3 times 15 is 45.
= √45
2 Simplify the root
Now we make √45 simpler, like in the lesson on square roots.
16 does not go into 45.
The biggest square that goes into 45 is 9: 45 divided by 9 is 5.
Square numbers: 4, 9, 16
45 ÷ 9 = 5 ✓
So √45 is √9 times √5.
= √9 × √5
√9 is 3, because 3 times 3 is 9.
3 × 3 = 9
So we get 3√5.
So √3 × √15 = 3√5.
= 3√5
3 Check
Let's check with a calculator.
The start is about 6.71.
Start: √3 × √15 ≈ 6.71
The answer is about 6.71 too.
So it is right!
Answer: 3√5 ≈ 6.71
Let's look back.
First: multiply.
Then: simplify the root.
Last: check.
Answer
= 3√5