Introduction to Number Systems

Classify the following number as rational or irrational:

$\sqrt{441}$

Every irrational number is a real number.

List all the elements of $A$ that are rational numbers.

$A=\left\{-2, 34, \sqrt{2}, \sqrt{9}, \mathrm{\pi }\right\}$

List all the subsets that $7.3$ lies in.

Every whole number is a natural number.

Express $\frac{5}{48}$ in decimal form.

Simplify: $3\frac{1}{4}-\left(7\frac{3}{4}-1\frac{1}{2}\right)÷1\frac{1}{4}$

Write whether the following statement is true or false. Give reasons:

Every natural number is a whole number.

Express $3.05$ as a fraction in simplest form.

Find the value of $x: x^2=7744$.

Find the value of $x: x^2=2304$.

Find the value of $x: x^2=225$.

Find one rational number between $\frac{1}{3}$ and $\frac{1}{2}$.

$A$ and $B$ can do a piece of work in $18$ days. If $A$ alone can do it in $24$ days, in how many days can $B$ alone do the same work?

Difference of two natural numbers is always

Every natural number is 

Find rational numbers $a$ and $b$ such that $\frac{2+5\sqrt{7}}{2-5\sqrt{7}} =a+ \sqrt{7}b$.

Insert $2$ rational numbers between $\sqrt{3}$ and $\sqrt{7}$.

Classify $2.\overline{18}$ as rational and irrational number.

Classify $\sqrt{7.29}$ as rational or irrational number.