Question

Find the smallest number by which each of the following must be multiplied and divided to obtain a fefect cube...... a) 675....

Answer 1

27 is answer of question

Answer 2

hye

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we have to Find the smallest number by which each of the following must be multiplied and divided to obtain a fefect cube...... a) 675....


so lets find the prime factorisation of 675

prime factorisation of 675 =   3 x 3 x 3 x 5 x 5 

 =>$\sqrt675} = \sqrt3 ^{2}* \sqrt{3} * \sqrt{5 ^{2} } }$

we see that 3 is not in pair 

=>∴ 3 is the smallest number divided/multiplied to 675 to make perfect square

=>3 ×675 =  2025
=>√2025 = 45

=> 675 ÷3 = 225
=>√225 = 15
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hope it helps u