Find the smallest no. by which …
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Sia ? 6 years, 5 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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