Square Root Squabble 3

When you divide a power of a number by its square root, it's the same as multiplying the previous power by the square root!

YX/√(Y) = YX-1√(Y); Y ≠ 0

(However, the variable Y can't be equal to zero because division by zero is undefined.)

Examples:

24/√(2) = 16/√(2) = 8√(2) = 11.3137085...

23 = 8; 4 - 1 = 3

36/√(3) = 729/√(3) = 243√(3) = 420.8883462...

35 = 243; 6 - 1 = 5

57/√(5) = 78,125/√(5) = 15,625√(5) = 34,938.56215...

56 = 15,625; 7 - 1 = 6

813/√(81) = 531,441/9 = 6,561 × 9 = 59,049

812 = 6,561; 3 - 1 = 2

(This time, Y = 81 & that number has a rational square root, which is 9!)

This math trick also works if Y is equal to an imaginary number or complex number! (The same thing with the variable X!)

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© Derek Cumberbatch