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hallm:

explain why any of the four operations (+ - x */.) places between the two terms 5 and -3 8 will result in an irrational number.

Mehek:

Could you add a picture so the question is clear?

hallm:

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Mehek:

Any idea?

hallm:

i have no idea

Mehek:

Do you know what irrational is

hallm:

no ma'am

Mehek:

An irrational number is a number that cannot be written as a fraction

Mehek:

So for example, 2 is rational because it can be written as 2/1 \(\sqrt{4}\) is rational because \(\sqrt{4}=2=\dfrac{2}{1}\) Can you tell me what \(\sqrt{8}\) = ?

hallm:

8 = 8/4 8/2 8/1 all of these are true right

Mehek:

you are correct

Mehek:

but here, they are asking for √8 not just 8

hallm:

i dont know then miss

Mehek:

Well, using a calculator √8 = 2.8284271...

Mehek:

The number cannot be put as a fraction because the number goes on and on

hallm:

wohhhh

Mehek:

And whether you add subtract, multiply, or divide 5 and -3√8, the answer will always be irrational because of the √8

hallm:

thats amazing

Mehek:

Unless if √8 is multiplied by some other number that's inside a radical. Such as √8 * √8 = √64 and square root of 64 is 8 But just multiplying it with 5 won't change the √8

hallm:

yes that is true i understand now thank you so much

Mehek:

You're welcome :)

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