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What is the smallest number by which 2925 must be divided so that the quotient is a perfect cube?with explanation. ​

Answer» <html><body><p>Answer:</p><p>We are given a <a href="https://interviewquestions.tuteehub.com/tag/number-582134" style="font-weight:bold;" target="_blank" title="Click to know more about NUMBER">NUMBER</a> 2925. We have to find the number by which 2925 <a href="https://interviewquestions.tuteehub.com/tag/must-2185568" style="font-weight:bold;" target="_blank" title="Click to know more about MUST">MUST</a> be divided to obtain a <a href="https://interviewquestions.tuteehub.com/tag/perfect-1150611" style="font-weight:bold;" target="_blank" title="Click to know more about PERFECT">PERFECT</a> square.</p><p>Firstly, prime factorize 2925.</p><p>2925 is an odd number so it is not divisible by 2. So start from the next prime which is 3.</p><p>2925 can be <a href="https://interviewquestions.tuteehub.com/tag/written-732709" style="font-weight:bold;" target="_blank" title="Click to know more about WRITTEN">WRITTEN</a> as three times 975.</p><p> 2925=3×975</p><p>975 can be written as three times 325.</p><p> 2925=3×3×325</p><p>325 can be written five times 65</p><p> 2925=3×3×5×65</p><p>65 can be written as five times 13.</p><p> 2925=3×3×5×5×132925=32×52×131</p><p>In the <a href="https://interviewquestions.tuteehub.com/tag/result-1187343" style="font-weight:bold;" target="_blank" title="Click to know more about RESULT">RESULT</a>, the exponent of 3 is 2 (even), the exponent of 5 is 2 (even) but the exponent of 13 is 1 which is odd. For a number to be a perfect square the primes in its prime factorization should have even exponents. So eliminate 13.</p><p>Therefore, 2925 must be divided by 13 to be a perfect square.</p><p>The perfect square will be 32×52=9×25=225</p><p>Now, find the square root of 225.</p><p> 225=32×52225−−−√=32×52−−−−−−√=3×5=15</p><p>15 is the square root of 225.</p><p>2925 must be divided by 13 to obtain a perfect square 225 and the square root of 225 is <strong>15.</strong></p><p></p></body></html>


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