Question

Find two irrational numbers between `4sqrt(2)` and `3sqrt(3)`.

Answer 1

Step 1: Approximate values

`4sqrt(2) = 4 xx 1.4142 = 5.6568`

`3sqrt(3) = 3 xx 1.732 = 5.196`

So the range is 5.196 < number < 5.6568.

Step 2: Check the given numbers

`sqrt(28) = 5.2915`,

`sqrt(29) = 5.3852`

Both clearly lie between 5.196 and 5.6568.

Two irrational numbers between `4sqrt(2)` and `3sqrt(3)` are `sqrt(28)` and `sqrt(29)`.