Question

Rationalize the denominator of sqrt32/(sqrt16-sqrt2). The answer can be written as )AsqrtB+C)/D, where A, B, C, and D are integers, D is positive, and B is not divisible by the square of any prime. Find the minimum possible value of A+B+C+D.

Answer 1

Explanation:

`(√(32) )/(√(16) - √(2) ) = (4√(2) )/(4 - √(2) ) ----------------- (1)`

It says it can be written in the form of

`(A√(B) + C )/(D)`

where A, B, C and D are integers, D is positive and B is not divisible by square of any prime

Rationalize equation 1:

`(4√(2) )/(4 - √(2) ) X (4 + √(2) )/(4 + √(2))`

in denominator, use (a + b)(a - b) =
`a^(2) - b^(2)`

After multiplying numerator and denominator you should get

`(16√(2) + 8)/(14)`

this is in the form

`(A√(B) + C )/(D)`

where A = 16, B = 2, C = 8, and D = 14

hope this helps you ^^