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Find the smallest no. by which 180 must be divided so that it becomes a perfect square. Also find the square root of the perfect square so obtained.

Posted by Riddhima Agarwal 6 years, 8 months ago

CBSE > Class 08 > Mathematics

1 answers

Sia ? 6 years, 8 months ago

The prime factorisation of 180 is 180 = 2 {tex}\times{/tex} 2 {tex}\times{/tex} 3 {tex}\times{/tex} 3 {tex}\times{/tex} 5
As the prime factor 5 has no pair, 180 is not a perfect square.
If 5 gets a pair, then the number will be a perfect square. So, we multiply 180 by 5 to get

180 {tex}\times{/tex} 5 = 2 {tex}\times{/tex} 2 {tex}\times{/tex} 3 {tex}\times{/tex} 3 {tex}\times{/tex} 5 {tex}\times{/tex} 5
No each prime factor has a pair. Therefore, 180 {tex}\times{/tex} 5 = 900 is a perfect square. Thus the required smallest number is 5.
Thus, {tex}\sqrt {900} {/tex} = 2 {tex}\times{/tex} 3 {tex}\times{/tex} 5 = 30.

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Posted by Monika 8B 9 months ago

CBSE > Class 08 > Mathematics