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## anonymous one year ago Which of the following numbers is irrational? negative 7 over 4, 2 over 3, square root of 3, square root of 4 a fraction with numerator negative 7 and denominator 4 a fraction with numerator 2 and denominator 3 square root of 3 square root of 4

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1. anonymous

help

2. UsukiDoll

$\LARGE -\frac{7}{4}, \frac{2}{3}, \sqrt{3},\sqrt{4}$ like this?

3. anonymous

yes @UsukiDoll

4. UsukiDoll

ok the definition of a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, p and q, with the denominator q not equal to zero. Since q may be equal to 1, every integer is a rational number.

5. UsukiDoll

irrational numbers can't be expressed as fractions. having square roots is a dead giveaway of an irrational number

6. UsukiDoll

an irrational number is any real number that cannot be expressed as a ratio of integers. Irrational numbers cannot be represented as terminating or repeating decimals.

7. UsukiDoll

$\LARGE e, \pi, \sqrt{2}$ are examples of irrational numbers.

8. UsukiDoll

so from this list $\LARGE -\frac{7}{4}, \frac{2}{3}, \sqrt{3},\sqrt{4}$ which of them are irrational?

9. anonymous

3

10. UsukiDoll

yes the square root of 3 is irrational

11. UsukiDoll

the square root of 4 can be simplified further into 2 and it's rational because it can be expressed as a fraction which is $\LARGE \frac{2}{1}$

12. UsukiDoll

$\LARGE \frac{2}{1} \rightarrow 2$

13. UsukiDoll

everything else is rational $\LARGE \sqrt{3}$ is irrational.

14. anonymous

thanks :) @UsukiDoll

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