# Irrational numbers questions and answers Recent questions in Irrational numbers
Irrational numbers
ANSWERED ### Prove or disprove that if a and b are rational numbers, then $$\displaystyle{a}^{{{b}}}$$ is also rational.

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

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

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

Irrational numbers
ANSWERED ### 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
ANSWERED ### Integers that are not whole numbers

Irrational numbers
ANSWERED ### Simplify the following: (a+10)(a+10)

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

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

Irrational numbers
ANSWERED ### 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
ANSWERED 