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dsp73
3 years ago
14

Write an counter example for the statement: all square roots are rational numbers

Mathematics
2 answers:
krok68 [10]3 years ago
5 0
That is not true. For example, if you take PI . Rounded is 3.14. But if you were to do the square root of pi then it would be an IRRATIONAL number. so it's false. <span />
olga_2 [115]3 years ago
3 0
It's false because if you take the square root of a decimal number or a complex number, you're sure to find an irrational number.
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First, plug-in x and y as 3sin​​θ-2 and 3cos​​​θ+4 into the equation, respectively:

((3\sin (\theta)-2)+2)^2 + ((3\cos (\theta)+4)-4)^2 = 9

Then, +2 and -2 cancel out and +4 and -4 cancel out as well, leaving you with:

(3\sin(\theta))^2+(3\cos(\theta))^2=9

We can factor out 3^2 = 9 from both equations:

9(\sin(\theta)^2+cos(\theta)^2) = 9

We know from a trigonometric identity that \sin(\theta)^2+cos(\theta)^2 = 1, meaning we can reduce the equation to:

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