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MATH / If we write √(2)+(1)/(√(2))+√(3)+(1)/(√(3)) in the form (a√(2)+b√(3))/(c) such that a, b, and c are positive integers and c is as small as possible, then what is a+b+c?

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

If we write

\sqrt{2}+\frac{1}{\sqrt{2}} + \sqrt{3} + \frac{1}{\sqrt{3}}

in the form

\dfrac{a\sqrt{2} + b\sqrt{3}}{c}

such that

a

b

, and

c

are positive integers and

c

is as small as possible, then what is

a+b+c

Plain-text mathematical notation (without MathML)

If we write √(2)+(1)/(√(2))+√(3)+(1)/(√(3)) in the form (a√(2)+b√(3))/(c) such that a, b, and c are positive integers and c is as small as possible, then what is a+b+c?

Original LaTeX notation

If we write $\sqrt{2}+\frac{1}{\sqrt{2}} + \sqrt{3} + \frac{1}{\sqrt{3}}$ in the form $\dfrac{a\sqrt{2} + b\sqrt{3}}{c}$ such that $a$, $b$, and $c$ are positive integers and $c$ is as small as possible, then what is $a+b+c$?

level

Level 4

type

Algebra

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task_id: b49ee8bc-ca5e-5dfd-b31f-7d3ae22205e7
task_key: algebra--test--b49ee8bc-ca5e-5dfd-b31f-7d3ae22205e7
task_revision_id: 2
config / split: algebra / test

Official source

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