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MATH / Rationalize the denominator of (√(5)+√(2))/(√(5)−√(2)). The answer can be written as (A+B√(C))/(D), where A, B, C, and D are integers, D is positive, and C is not divisible by the …

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problem

Rationalize the denominator of 5+25−2\frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}}. The answer can be written as A+BCD\frac{A+B\sqrt{C}}{D}, where AA, BB, CC, and DD are integers, DD is positive, and CC is not divisible by the square of any prime. If the greatest common divisor of AA, BB, and DD is 1, find A+B+C+DA+B+C+D.
Plain-text mathematical notation (without MathML)
Rationalize the denominator of (√(5)+√(2))/(√(5)−√(2)). The answer can be written as (A+B√(C))/(D), where A, B, C, and D are integers, D is positive, and C is not divisible by the square of any prime. If the greatest common divisor of A, B, and D is 1, find A+B+C+D.
Original LaTeX notation
Rationalize the denominator of $\frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}}$. The answer can be written as $\frac{A+B\sqrt{C}}{D}$, where $A$, $B$, $C$, and $D$ are integers, $D$ is positive, and $C$ is not divisible by the square of any prime. If the greatest common divisor of $A$, $B$, and $D$ is 1, find $A+B+C+D$.

level

Level 4

type

Algebra

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Source and history

task_id
b1521fd5-294c-5ea9-b176-0475ab0294ec
task_key
algebra--test--b1521fd5-294c-5ea9-b176-0475ab0294ec
task_revision_id
1
config / split
algebra / test

Official source

initial import