Question

given that 8-sqrt(18) over sqrt(2) = a + b sqrt(2) where a and b are integers find the value of a and b

Answer 1

a = -3, b = 4.

Explanation:

(8 - √18) / √2

= (8 - 3√2) √2

= 8/√2 - 3

= 8√2 / 2 - 3

= -3 + 4√2

So a + b√2 = -3 + 4√2

Comparing coefficients we have:

a = -3 and b = 4 (answer).

Answer 2

a = - 3 and b = 4

Explanation:

Given

`(8-√(18) )/(√(2) )`

Simplify
`√(18)`

=
`√(9(2))` =
`√(9)` ×
`√(2)` = 3
`√(2)`

Thus expression can be written as

`(8-3√(2) )/(√(2) )`

Multiply numerator/denominator by
`√(2)`

noting that
`√(2)` ×
`√(2)` = 2

=
`(√(2)(8-3√(2))  )/(√(2)(√(2))  )`

=
`(8√(2)-6 )/(2)`

Dividing each term on the numerator by 2

= 4
`√(2)` - 3

= - 3 + 4
`√(2)`

with a = - 3 and b = 4