Question

Is 920 a perfect cube ? If not , Find the smallest number by which it should be multiplied to get a perfect cube .

Answer 1

$\huge{\mathfrak{\underline{\underline{Answer :-}}}}$

$\large{\bf{Cubes}}$

$\begin{array}{r | 1}</p><p> </p><p> 2 & 920 \\</p><p>\cline{ 2 - 2} 2 & 460 \\</p><p>\cline{ 2 - 2} 2 & 230 \\ </p><p>\cline{ 2 - 2} 5 & 115 \\</p><p>\cline{ 2 - 2} 23 & 23 \\</p><p>\cline{ 2 - 2} & 1 \\</p><p></p><p></p><p>\end{array}</p><p></p><p>$

$\large{\bf{ <u>2</u> * <u>2</u> * <u>2</u> * 5 * 23}}$

$\large{\sf{It \: is \: not \: a \: perfect \: cube}}$

$\huge{\bf{Verification}}$

$\large{\sf{In \: a \: perfect \: cube \: there \:are\:three \: pairs.}}$

$\large{\sf{ So, \: to \: make \: it \: perfect \: cube \: we \: will \: make \: the \: three \: pairs \: of 5 \: and \: 23}}$

$\huge{\bf{Hence,}}$

$\large{\sf{We, \:will \:multiply \:them \:with 5 * 5 * 23 * 23}}$

$\large{\mathbf{\star{\boxed{We \: must \: multiply \: it \: by \: {\underline{13,225}}}}}}$

Answer 2

Answer:

920 × 5×5×23×23 = (2×5×23)³

=(230)³ /*perfect cube

Step-by-step explanation:

Resolving 920 into prime factors,we get

2|920

________

2|460

________

2|230

________

5|115

________

***23

920 = 2×2×2×5×23

The prime factors 5,23 doesn't appear in a group of three factors.

So, 920 is not a perfect cube.

Hence , the smallest number by which it is to be multiplied to make it a perfect cube is 5×5×23×23 = 13225

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