Rational and Irrational Numbers

On a number line, if point A is at $-2$ and point B is at $2$, what is the midpoint of AB?

Which of these numbers is represented by the same point as $0.5$ on the number line?

The point representing $\frac{1}{2} + \frac{1}{4}$ on the number line is:

Which integer is closest to $-\sqrt{5}$ on the number line?

Which of the following irrational numbers is between $3.1$ and $3.2$ on the number line?

Where is the number $\sqrt{0.5}$ located on the number line?

In constructing $\sqrt{21}$ on the number line, if a student uses a base of $4$ units, what irrational length must the perpendicular have?

In successive magnification, every real number can be represented on the number line because of:

The number $\sqrt{2} - \sqrt{3}$ on the number line is located:

If we represent $\sqrt{10.5}$ geometrically, what is the length of the radius of the semicircle used?

Which of the following is an irrational number between $1$ and $2$?

The decimal $0.5$ is a rational number. Its $p/q$ form is:

The multiplicative inverse of $-5$ is:

If we multiply an irrational number by $0$, the result is:

Which of the following correctly arranges the surds $\sqrt{2}$, $\sqrt[3]{3}$, and $\sqrt[6]{6}$ in ascending order?

Find the value of the following expression: $(\sqrt[3]{4} - 1)(\sqrt[3]{16} + \sqrt[3]{4} + 1)$.

If $x = \sqrt{7} + \sqrt{3}$ and $y = \sqrt{7} - \sqrt{3}$, find the value of $x^2 + y^2$.

If $x = \frac{\sqrt{m+n} + \sqrt{m-n}}{\sqrt{m+n} - \sqrt{m-n}}$, find the value of the expression $\frac{nx^2 + n}{mx}$.

If the expression $\frac{1}{\sqrt{2} + \sqrt{3} - \sqrt{5}}$ is rationalized and written in the form $\frac{a\sqrt{2} + b\sqrt{3} + c\sqrt{30}}{12}$, where $a, b,$ and $c$ are integers, find the value of $a \times b \times c$.

Simplify the expression: $\frac{1}{\sqrt{12-\sqrt{140}}} - \frac{1}{\sqrt{8-\sqrt{60}}} - \frac{2}{\sqrt{10+\sqrt{84}}}$

The simplified form of $\sqrt{128}$ is:

What is the simplest rationalizing factor of $\sqrt{32}$?

The value of $\sqrt[3]{8} \times \sqrt[3]{1}$ is:

The rationalizing factor of $x + \sqrt{y}$ is:

Rationalize the denominator: $\frac{\sqrt{13} - \sqrt{11}}{\sqrt{13} + \sqrt{11}}$

If $x = 4 - \sqrt{15}$, find the value of $(x + \frac{1}{x})^2$.

Evaluate: $(3\sqrt{5} + 2\sqrt{2})(3\sqrt{5} - 2\sqrt{2})$

Simplify the expression: $\frac{3\sqrt{2}}{\sqrt{6} - \sqrt{3}} - \frac{4\sqrt{3}}{\sqrt{6} - \sqrt{2}} + \frac{2\sqrt{3}}{\sqrt{6} + 2}$.

Rationalize the denominator: $\frac{1}{\sqrt[3]{2} + 1}$.

Find the simplest rationalizing factor of $\sqrt{18} - \sqrt{50}$.