Question

find the smallest number for which the number 243 should be multiplied to obtain a perfect cube

Answer 1

Step-by-step explanation:

it is also a cube

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Answer 2

$\huge\tt{\underline{\underline{Solution:}}}$

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$\sf\small\blue{Prime\: factorizing\: 243,\: we \:get,}$

• $\sf\small\red{243\:=\:3\:×\:3\:×\:3\:×\:3\:×\:3\:=\:3⁵.}$

$\sf\small\pink{We \:know, \:a\: perfect \:cube \:has\: multiples\:of\:3\:as}$$\sf\small\pink{powers \:of\: prime\: factors.}$

• $\sf\small\green{Here, \:number \:of\: 3's \:is\: 5.}$

$\sf\small\orange{So\: we\: need\: to\: multiply \:another\: 3\:in\:the}$$\tt\small\orange{ factorization\: to\: make\: 243 \:a \:perfect}$$\tt\small\orange{cube.}$

$\tt\small\purple{Hence,\: the \:smallest \:number\: by \:which \:243}$$\tt\small\purple{must\:be \:multiplied \:to \:obtain \:a \:perfect \:cube \:is }$$\tt\small\purple{3.}$

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