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MATH / The number √(104√(6)+468√(10)+144√(15)+2006)can be written as a√(2)+b√(3)+c√(5), where a, b, and c are positive integers. Find a⋅b⋅c.

Problem

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

problem

The number 1046+46810+14415+2006\sqrt{104\sqrt6+468\sqrt{10}+144\sqrt{15}+2006}can be written as a2+b3+c5a\sqrt2+b\sqrt3+c\sqrt5, where aa, bb, and cc are positive integers. Find a⋅b⋅c.a\cdot b\cdot c.
Plain-text mathematical notation (without MathML)
The number √(104√(6)+468√(10)+144√(15)+2006)can be written as a√(2)+b√(3)+c√(5), where a, b, and c are positive integers.  Find a⋅b⋅c.
Original LaTeX notation
The number $$\sqrt{104\sqrt6+468\sqrt{10}+144\sqrt{15}+2006}$$can be written as $a\sqrt2+b\sqrt3+c\sqrt5$, where $a$, $b$, and $c$ are positive integers.  Find $a\cdot b\cdot c.$

level

Level 3

type

Intermediate Algebra

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Source and history

task_id
aecad327-7d68-5c56-ad7e-12dfd98b1264
task_key
intermediate~5falgebra--test--aecad327-7d68-5c56-ad7e-12dfd98b1264
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import