Math, asked by clashermalik, 1 year ago

find the smallest number by which 1372 may be multiplied so that the product is a perfect cube

Answers

Answered by amankumaraman11
10
Hey There! Your Solution Is In The Attachment↓↓↓↓↓








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Attachments:

VemugantiRahul: check ! its 7 not 2
amankumaraman11: No ! Its 2 not 7, And Your solution is totally wrong..
Answered by VemugantiRahul
6
\mathfrak{\huge{\orange{\underline{\blue{Hola\: !}}}}}

\mathbb{\underline{\green{Type\: Of\: Problem:}}}

¶ To find the smallest No. by which a No. (Say N) be multiplied so that the resultant product is a perfect square

\mathbb{\underline{\green{Approach\: To\: Problem:}}}

¶ Steps:

• Resolve N into product of Prime factors
• Express them in Exponential Form with prime factors having power as 2.
• Required least No. is the prime factor(or product of prime factors) which are not having 2 as their power.

\mathcal{\underline{\purple{SOLUTION:}}}

Given,
N = 1372

Using Prime Factorisation,
2 | 1372
2 | 686
7 | 343
7 | 49
.• | 7

•°• 1372 = 2 × 2 × 7 × 7 × 7

In exponential form,
1372 = 2^{2} × 7^{2} × 7

To get a perfect square, 1372 is to be multiplied by 7.

•°• \underline{\underline{Required\: least\: No.\: = 7}}

\mathfrak{\huge{\pink{Cheers}}}

\mathcal{\huge{\orange{Hope\: it\: Helps}}}
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