Question

Which is greater?

`3sqrt(5)` and `6sqrt(2)`

Answer 1

Given: Compare `3sqrt(5)` and `6sqrt(2)`.

Step-wise calculation:

1. Calculate the approximate value of each term:

`3sqrt(5) = 3 xx sqrt(5)`

`6sqrt(2) = 6 xx sqrt(2)`

2. Use approximate values for the square roots:

`sqrt(5) ≈ 2.236`

`sqrt(2) ≈ 1.414`

3. Calculate each:

`3sqrt(5) = 3 xx 2.236 = 6.708`

`6sqrt(2) = 6 xx 1.414 = 8.484`

4. Compare:

6.708 < 8.484

`6sqrt(2)` is greater than `3sqrt(5)`.

So, `6sqrt(2) > 3sqrt(5)`.