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1)FIND THE LEAST NUMBER BY WHICH 3528 SHOULD BE MULTIPLIED TO GET A PERFECT SQUARE.
2)FIND THE LEAST NUMBER BY WHICH 5000 SHOULD BE DIVIDED TO GET A PERFECT CUBE.
3)FIND THE LEAST NUMBER BY WHICH 180 SHOULD BE DIVIDED TO GET A PERFECT SQUARE.

Answer :

kooper
1)Firstly, factorize 3528.
3528 = 2 * 2 * 2 *3 * 3 * 7 * 7.
Now we know that a perfect square should have a pair of two prime factor.
This number has 1 pair of 2, 1 pair of 3, 1 pair of 7 and 1 alone factor 2.
Therefore, this number has a 2 less. So, 2 must be multiplied in 3528 to get a perfect square.

2)Firstly, factorize 5000.
5000 = 2 * 2 * 2 * 5 * 5 * 5 * 5.
Now we know that a perfect cube should have a pair of three prime factor.
This number has 1 pair of 2, 1 pair of 5 and 1 alone factor 5.
Therefore, this number has a 5 more. So, 5 must be divided in 5000 to get a perfect cube.

3)Firstly, factorize 180.
180 = 2 * 2 * 3 * 3 * 5.
Now we know that a perfect square should have a pair of two prime factor.
This number has 1 pair of 2, 1 pair of 3 and 1 alone factor 5.
Therefore, this number has a 5 more. So, 5 must be divided in 180 to get a perfect square.
Sol-1> 3528*2=7056. Sq root of 84.
Sol-2>5000*25=125000. cube root of 50
Sol-3>180*5=900. Sq root of 30. 
Hope this helps you.........

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