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find the smallest number by which the given number must be divided so that the quotient is a perfect square.Also find the number whose square is the new number:-
1)12150
i just donno this one
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- David O. McKay
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By breaking it down into its prime factors, we get 12150 = 2 * 3[sup]5[/sup] * 5[sup]2[/sup].
We can determine the biggest square factor of 12150 by taking as many matching pairs as we can out of its decomposition. That would be 3[sup]4[/sup] * 5[sup]2[/sup]. We are then left with 2*3 = 6.
Therefore, 6 is the smallest number that you can divide 12150 by to produce a square, and trying that out shows that we produce the square of 45.
Why did the vector cross the road?
It wanted to be normal.
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For the first part
find the smallest number by which the given number must be divided so that the quotient is a perfect square.
it depends on the number. If the number is a perfect square, you divide by 1; if the number has no repeated factors, divide the number by itself (so the quotient is 1 = 1²). If the number is not a perfect square and has repeated factors, pair off all the repeated factors and divide it by the remaining (non-repeated) factors. (For example, for 96 = (2×2)×(2×2)×2×3, divide it by 2×3 = 6.)
Last edited by JaneFairfax (2007-03-15 04:52:31)
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Right~Exactly
Numbers are the essence of the Universe
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thanks.i got it now
"Let us realize that: the privilege to work is a gift, the power to work is a blessing, the love of work is success!"
- David O. McKay
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