Question

Is √13 + 4 rational or irrational?

Answer 1

Hi student, let me help you out! :)

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We are asked to find out if $\pmb{\sqrt{13} +4}$ is rational or irrational.

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• Irrational numbers cannot be expressed as fractions (in $\pmb{\cfrac{p}{q}}$ form).

So, can we write $\pmb{\sqrt{13} +4}$ as a fraction? We can write 4 as a fraction, but we cannot write $\pmb{\sqrt{13}}$ as a fraction, because this number has infinitely many digits after the decimal point, and they never repeat; there's no pattern at all!

And even if we add 4, which is a rational number, to $\pmb{\sqrt{13}}$, we'll still get an irrational number.

Thus, $\pmb{\sqrt{13}+4}$ is irrational.

Hope it helps you out! :D

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Answer 2

Answer:

irrational

Step-by-step explanation:

what are rational numbers ?

every number that can be expressed as a/b, with a and b being integer numbers, and b different to 0.

the square root of any number that is not a squared rational number is then an irrational number.

I am not sure, if the expression here is

sqrt(13) + 4

or

sqrt(13 + 4), which would then be sqrt(17).

but in both cases we are creating the square root of a not- squared rational number.

neither 13 nor 17 are the result of a multiplication of a rational number with itself.

in fact, 13 and 17 are prime numbers with no other factors than either 1 or themselves.

so, both, sqrt(13) and sqrt(17) are irrational numbers.

adding or subtracting rational numbers to irrational numbers result again in irrational numbers.