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#1 2007-03-15 04:31:04

soha
Real Member
Registered: 2006-07-07
Posts: 2,530

hhhhhhhhhhhhheeeeeeeeeeeelllppppp!!!!

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 dunno


"Let us realize that: the privilege to work is a gift, the power to work is a blessing, the love of work is success!" smile smile
- David O. McKay

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#2 2007-03-15 04:36:21

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: hhhhhhhhhhhhheeeeeeeeeeeelllppppp!!!!

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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#3 2007-03-15 04:48:21

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: hhhhhhhhhhhhheeeeeeeeeeeelllppppp!!!!

For the first part

soha wrote:

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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#4 2007-03-15 05:32:12

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

Re: hhhhhhhhhhhhheeeeeeeeeeeelllppppp!!!!

Right~Exactly


Numbers are the essence of the Universe

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#5 2007-03-15 06:12:10

soha
Real Member
Registered: 2006-07-07
Posts: 2,530

Re: hhhhhhhhhhhhheeeeeeeeeeeelllppppp!!!!

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!" smile smile
- David O. McKay

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