Find the smallest number by which 2400 is to be multiplied to get a perfect square and also find the square root of the resulting number.
Answers
Answer :-
Prime factorization of 2400,
2 | 2400
|__________
2 | 1200
|__________
2 | 600
|__________
2 | 300
|__________
2 | 150
|__________
3 | 75
|__________
5 | 25
|__________
5 | 5
|__________
| 1
|
2400 = 2 × 2 × 2 × 2 × 2 × 3 × 5× 5
There are one 2 and one 3 in the above which are without any pair.
Therefore, smallest number is 2×3 = 6, by which 2400 is to be multipled to get a perfect square.
Resulting number = 2400 × 6 = 14400
Square root of 14400 is
120
__________
1 | 14400
| 1
|__________
22 | 044
| 44
|__________
| 000
|__________
Hence, √14400 = 120
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