# Irrational numbers questions and answers

Recent questions in Irrational numbers
Irrational numbers

### Prove or disprove that if a and b are rational numbers, then $$\displaystyle{a}^{{{b}}}$$ is also rational.

Irrational numbers

### Prove or disprove that the product of two irrational numbers is irrational.

Irrational numbers

### Explain why the sum, the difference, and the product of two rational numbers are rational numbers. Is the product of two irrational numbers necessarily irrational? What about the sum?

Irrational numbers

### Find a) a rational number and b) a irrational number between the given pair. $$\displaystyle{3}\frac{{1}}{{7}}$$ and $$\displaystyle{3}\frac{{1}}{{6}}$$

Irrational numbers

### Discover prove: Combining Rational and Irrationalnumbers is $$\displaystyle{1.2}+\sqrt{{2}}$$ rational or irrational? Is $$\displaystyle\frac{{1}}{{2}}\cdot\sqrt{{2}}$$ rational or irrational? Experiment with sums and products of ther rational and irrational numbers. Prove the followinf. (a) The sum of rational number r and an irrational number t is irrational. (b) The product of a rational number r and an irrational number t is irrational.

Irrational numbers

### 1) Find 100 irrational numbers between 0 and $$\displaystyle\frac{{1}}{{100}}.$$ 2) Find 50 rational numbers betwee 1 and 2. 3) Find 50 irrational numbers betwee 1 and 2.

Irrational numbers

### Prove that the set of irrational numbers in [0,1] is not countable

Irrational numbers

### Find the value of the following expression: $$\displaystyle{4}\sqrt{{2}}+{2}{\left(\sqrt{{36}}-\sqrt{{8}}\right)}$$

Irrational numbers

### Which statement is false? A. every irrational number is also a real number. B. every integer is also a real number. C. no irrational number is irrational. D. every integer is also an irrational number.

Irrational numbers

### Integers that are not whole numbers

Irrational numbers

### Simplify the following: (a+10)(a+10)

Irrational numbers

### Determine whether the below given statement is true or false. If the statement is false, make the necessary changes to produce a true statement: All irrational numbers satisfy |x - 4| > 0.

Irrational numbers

### Consider the following statements. Select all that are always true. The sum of a rational number and a rational number is rational. The sum of a rational number and an irrational number is irrational. The sum of an irrational number and an irrational number is irrational. The product of a rational number and a rational number is rational. The product of a rational number and an irrational number is irrational. The product of an irrational number and an irrational number is irrational.

Irrational numbers

### In which set(s) of numbers would you find the number $$\displaystyle\sqrt{{80}}$$ - irrational number - whole number - rational number - integer - real number - natural number

Irrational numbers

### Cindy separated her fruit flies into equal groups. She estimates that there are 2¹⁰ fruit flies in each of 2² jars. How many fruit flies does Cindy have in all?

Irrational numbers

### Given each set of numbers, list the a) natural Numbers b) whole numbers c) integers d) rational numbers e) irrational numbers f) real numbers $$\displaystyle{\left\lbrace-{6},\sqrt{{23}},{21},{5.62},{0.4},{3}\frac{{2}}{{9}},{0},-\frac{{7}}{{8}},{2.074816}\ldots\right\rbrace}$$

Irrational numbers

### To find the equation $$4\sqrt{8}\times\sqrt{10}=?$$

Irrational numbers

### Find the outcome of: $$\displaystyle{\cos{{\left(\frac{\pi}{{4}}+\frac{\pi}{{3}}\right)}}}$$

Irrational numbers

### The rational numbers are dense in $$\displaystyle\mathbb{R}$$. This means that between any two real numbers a and b with a < b, there exists a rational number q such that a < q < b. Using this fact, establish that the irrational numbers are dense in $$\displaystyle\mathbb{R}$$ as well.

Irrational numbers