Question

If `sqrt(2) = 1.414`, find the value of the following:

`3sqrt(72) + 6sqrt(128) - sqrt(288)`

Answer 1

Given: `sqrt(2) = 1.414`

We need to find the value of `3sqrt(72) + 6sqrt(128) - sqrt(288)`

Step-wise calculation:

1. Simplify each square root term:

`sqrt(72) = sqrt(36 xx 2) = 6sqrt(2)`

`sqrt(128) = sqrt(64 xx 2) = 8sqrt(2)`

`sqrt(288) = sqrt(144 xx 2) = 12sqrt(2)`

2. Substitute back into the expression:

`3(6sqrt(2)) + 6(8sqrt(2)) - 12sqrt(2)`

= `18sqrt(2) + 48sqrt(2) - 12sqrt(2)`

3. Combine like terms:

`(18 + 48 - 12)sqrt(2) = 54sqrt(2)`

4. Calculate using the given approximate value of `sqrt(2)`:

54 × 1.414 = 76.356

The value of the expression is approximately 76.356.