Which of the following numbers is not rational?

1 answer:

Feliz [49]2 years ago

3 0

Answer: √5

2.7 is a rational number because it's a terminating decimal which means that the decimal does end and all terminating decimals are rational numbers.

-3 is a rational number because it's an

integer and all integers are rational.

√4 is rational because it's a perfect square which means that a number can be multiplied by itself to get 4 and that number is 2.

√5 is no rational! It's impossible to find a whole number multiplied by itself to give us 5 which means that it's

non-terminating and non-repeating.

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Sedbober [7]

By the polynomial remainder theorem, because x = 2i is a zero of f(x), we have no remainder upon dividing f(x) by x - 2i.

Computing the quotient yields

$\dfrac{x^4+x^2+a}{x-2i} = x^3+2ix^2-3x-6i+\dfrac{12+a}{x-2i}$

Then if the remainder term is 0, follows that a = -12.

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