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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.

User Simendsjo
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1 Answer

4 votes

Answer:

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 ^^

User Grender
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