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, the smallest number is 2*3 = 6, by which 2400 is to be multiplied to get a perfect square.
Resulting number = 2400*6 = 14400
Square root of 14400
120
___________
1 |14400
|1
|_____
22 |044
| 44
|______
| 000
|______
Hence, √14400 = 120
Answer.
Step-by-step explanation:
Answer:
The smallest number by which 2400 is to be multiplied to get perfect square is 6 and the square root of the resulting number is 120
Step-by-step explanation:
Given: Number = 2400
To Find : Find the smallest number by which 2400 is to be multiplied to get perfect square and also find the square root of the resulting number
Solution:
Number = 2400
Prime factorization of 2400
2 |2400
|_________
2 |1200
|_________
2 | 600
|_________
2 | 300
|_________
2 | 150
|_________
3 | 75
|_________
5 | 25
|_________
5 | 5
|_________
| 1
2400=2 \times 2 \times 2\times 2 \times 2 \times 3 \times 5 \times 52400=2×2×2×2×2×3×5×5
2400=2^2 \times 2^2 \times 2 \times 3 \times 5^22400=2
2
×2
2
×2×3×5
2
3 \times 2 =63×2=6
So, 6 is the least number which should be multiplied to get perfect square
So, the resulting number is 2400 \times 6 =144002400×6=14400
So, \sqrt{14400}=120
14400
=120
Hence the smallest number by which 2400 is to be multiplied to get perfect square is 6 and the square root of the resulting number is 120
Step-by-step explanation:
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