Elements of Algebra

Cover Elements of Algebra
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Find m so that 9 a* + 12 a' + 10 a^ + ma + 1 shall be a perfect square.
20. Show that the square root of 2[(m + ?i)*+(m^ + ?i*)] is 2 (m" + w" + mw).
FACTORS. 99 131. The square roots of numbers are similarly found.
Eequu-ed the square root of 547.56.
Eoot =2 3. 4 Power = 5'47.56 contains f' + 2fn + •»?■ f^ = 4 00.00 2/i =40 147.66 " 2/i9»i + V /i = 20 2/i + wi = 43 1 29.00 = " wi= 3 2/2 = 46 18.56 contains 2/2^2 + n^ f^ = 23 2/2 + % = 46.4 18.56 = " wa= 0.4 Explanation. 1. •.■ the highest orde
...r of the power is lOO's, the highest order of the root is lO's, and it is unnecessary to look below lOO's for the square of lO's.
2. Similarly, it is unnecessary to look below I's for the square of I's, below lOOths for the square of lOths, etc.
3. The greatest square in the lOO's is 400, which is the square of 20, which may be called /i (read "/-one "), the first found part.
4. Subtracting, 147.56 contains 2/re + rfi, because /^ has been sub- tracted from/2 + 2/w + rfi, where / stands always for the found part and n for the next order of the I'oot.


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