Question

17. Find the smallest number by which 675 must be multiplied to obtain a perfect cube.​

Answer 1

Answer⤵️

675 = 3×3×3×5×5

Grouping the prime factors of 675 to triples , we are left over with 5×5 .

Therefore , 675 is not a perfect cube.

Now, {675} ×5 = [ 3×3×3×5×5 ] ×5 or

3375 = 3×3×3×5×5×5

Now , 3375 is a perfect cube .

Thus , the smallest no. is required no. to multiply 675 such that the no. perfect

cube is 5.

@ll the best :)