Question

Arrange in ascending order.

`2sqrt(7), 3sqrt(2), 4sqrt(3)`

Answer 1

Given: `2sqrt(7), 3sqrt(2), 4sqrt(3)`

Stepwise calculation:

1. Evaluate or compare their approximate values by expressing each as a single square root:

`2sqrt(7) = sqrt(4 xx 7)`

= `sqrt(28) ≈ 5.2915`

`3sqrt(2) = sqrt(9 xx 2)`

= `sqrt(18) ≈ 4.2426`

`4sqrt(3) = sqrt(16 xx 3)`

= `sqrt(48) ≈ 6.9282`

2. Sort these approximate values in ascending order:

`sqrt(18) < sqrt(28) < sqrt(48)`

⇒ `3sqrt(2) < 2sqrt(7) < 4sqrt(3)`

So, the numbers in ascending order are `3sqrt(2) < 2sqrt(7) < 4sqrt(3)`.