Question

Arrange in ascending order.

`7sqrt(2), 3sqrt(11), 5sqrt(3)`

Answer 1

Given: `7sqrt(2), 3sqrt(11), 5sqrt(3)`

Stepwise calculation:

1. Compute the approximate decimal values of each term using the approximate values `sqrt(2) ≈ 1.414, sqrt(3) ≈ 1.732` and `sqrt(11) ≈ 3.317`:

`7sqrt(2) = 7 xx 1.414 = 9.898`

`3sqrt(11) = 3 xx 3.317 = 9.951`

`5sqrt(3) = 5 xx 1.732 = 8.660`

2. Arrange these numerical values in ascending order:

`8.660(5sqrt(3)) < 9.898 (7sqrt(2)) < 9.951 (3sqrt(11))`

The ascending order of the given expressions is `5sqrt(3) < 7sqrt(2) < 3sqrt(11)`.