Question

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

`sqrt(200) + sqrt(50) - 5sqrt(32)`

Answer 1

Given: `sqrt(2) = 1.414`

Find the value of `sqrt(200) + sqrt(50) - 5sqrt(32)`

Step-wise calculation:

1. Simplify each square root term:

`sqrt(200) = sqrt(100 xx 2) = 10sqrt(2)`

`sqrt(50) = sqrt(25 xx 2) = 5sqrt(2)`

`sqrt(32) = sqrt(16 xx 2) = 4sqrt(2)`

2. Substitute these back into the expression:

`sqrt(200) + sqrt(50) - 5sqrt(32)`

= `10sqrt(2) + 5sqrt(2) - 5 xx 4sqrt(2)`

= `10sqrt(2) + 5sqrt(2) - 20sqrt(2)`

= `(10 + 5 - 20)sqrt(2)`

= `-5sqrt(2)`

3. Use the given `sqrt(2) = 1.414`:

`-5sqrt(2)`

= –5 × 1.414

= –7.07

So, the value of `sqrt(200) + sqrt(50) - 5sqrt(32)` is –7.07 when `sqrt(2) = 1.414`.