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Square Root of Squares

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by Abhishek009 » Mon Jun 04, 2012 7:34 am
iconlon wrote:What is the fastest way to solve?

Sqrt[(125,000)^2 - (35,000)^2]
[(125,000)^2 - (35,000)^2] is in the form of ( a^2 - b^2 )

=> ( a + b ) ( a - b )

=> 160000 * 90000

Now use the root -

Sqrt[(125,000)^2 - (35,000)^2]

=>Sqrt[160000 * 90000]

=> 400*300

=> 120000
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by iconlon » Mon Jun 04, 2012 7:37 am
I know I can use the following method, but I feel like there has to be a quicker way...

Sqrt[(125,000)^2 - (35,000)^2]
=Sqrt[(2^3*5^6)^2 - (2^3*5^4*7)^2]
=Sqrt[(2^6*5^12) - (2^6*5^8*7^2)]
=Sqrt[(2^6*5^8)*(5^4-7^2)]
=2^3*5^4 * Sqrt[5^4 - 7^2]
=5,000 * Sqrt (2^6 * 3^2)
=5,000 * 2^3 * 3
=120,000
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by iconlon » Mon Jun 04, 2012 7:38 am
Ah, thanks Abhishek009, this is much quicker.
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