what is the smallest perfect square that is greater than 20,0000 and is divisible by 392
2007-02-24 06:48:50 · 9 answers · asked by asdfasdffdas 1 in Science & Mathematics ➔ Mathematics
perhaps you meant 20,000
that would be 50,176
2007-02-24 06:53:42 · answer #1 · answered by 7 · 0⤊ 0⤋
The comma in 20,0000 is confusing - I'll provide information for both 200,000 and 20,000.
392 is 2^3 * 7^2, so for N^2 to be divisible by 392, N must be divisible by 2^2 * 7 = 28.
Sqrt( 200,000 ) = 447.21... and 448 is divisible by 28, so 448^2 = 200,704 is your answer.
Sqrt( 20,000 ) = 141.42... and the smallest integer >141.42 divisible by 28 is 168, so the answer in this case is 28,224,
2007-02-24 07:02:24 · answer #2 · answered by Anonymous · 0⤊ 0⤋
You need to clarify your question. Are you talking greater that 200,000 with a misplaced coma or maybe 20,000 with an extra zero inadvertently added. 200704 is divisible by 392 and is the square of 448. 28224 is divisible by 392 and is the square of 168.
2007-02-24 07:31:14 · answer #3 · answered by Anonymous · 0⤊ 0⤋
392 = (2^3)(7^2)
If the number you gave is 20,000, then the smallest perfect square would be (6^2)(2^4)(7^2) = 28,224
If the number you gave is 200,000, then the smallest perfect square would be (16^2)(2^4)(7^2) = 200,704
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Reason:
Since (2^4)(7^2) = 784 must be a factor, and 20,000/784 = 25.51 or 200,000/784 = 255.1, the problem is simplified to find the smallest perfect square which is greater than 25.51 or 255.1 respectively.Therefore, I found 6^2 = 36 is the smallest perfect square greater than 25.51 and 16^2 = 256 is the smallest perfect square greater than 255.1.
2007-02-24 06:57:00 · answer #4 · answered by sahsjing 7 · 0⤊ 0⤋
28224
I did this the lazy way, you know it has to be a multiple of 392 and greater than 20 000, so divide 20 000 by 392 to get your starting point (52) and then start multiply 392 by 52, then 53, then 54, etc, and take the sq root of each. you stike pay dirt when you get one without a decimal after it.
2007-02-24 07:00:40 · answer #5 · answered by Anonymous · 0⤊ 0⤋
I understand that you wrote 200,000.In this case it would be
2^12*7^2 =200,704 which is the square of448 ans divided 392 gives 512
2007-02-24 07:20:20 · answer #6 · answered by santmann2002 7 · 0⤊ 0⤋
200,704 (square of 448). Dividing by 392 gives you 512.
2007-02-24 06:54:57 · answer #7 · answered by TheOnlyBeldin 7 · 0⤊ 0⤋
I didn't know if you mean 20,000 or 200,000 - so, here is the answer for both:
20,000: 168^2 = 28,224. 28,224 / 392 = 72
200,000: 448^2 = 200,704. 200,704 / 392 = 512
2007-02-24 06:56:27 · answer #8 · answered by Sidewinder 3 · 0⤊ 0⤋
It's either 50,176 or 200,704 dependig upon whether you meant 20,000 or 200,000.
2007-02-24 07:06:15 · answer #9 · answered by ironduke8159 7 · 0⤊ 1⤋