The World of Numbers

Which of the following is a rational number?

The negative of $0$ is:

If $x + 5 = 5$, what is the value of $x$?

The concept of zero was essential for the development of which system of notation?

Which mathematician's name is associated with the 'Sieve' method for finding prime numbers?

What is the product of $(2 + \sqrt{2})$ and $(2 - \sqrt{2})$?

Simplify: $4\sqrt{3} + 3\sqrt{3}$.

In the revolution of 'Śhūnya', if we define a number as $x = 0.\overline{9}$, what is the exact value of $x$ in integer form?

Find the value of $(256)^{0.16} \times (256)^{0.09}$.

If $x = \frac{1}{2-\sqrt{3}}$, find the value of $x^2 - 4x + 1$.

Calculate: $(-10) + (-20) + 30$.

What is the product of $0$ and any negative integer?

Which of the following is equal to $(-3) \times [4 + (-2)]$?

Identify the integer which is its own additive inverse.

A student was tasked with multiplying an integer by $-2$ and then adding $10$ to the product. Instead, the student divided the integer by $-2$ and then subtracted $10$ from the quotient, resulting in a final value of $-6$. If the student had followed the original instructions correctly, what would the result have been?

If $a = -2$, find the value of $a^3 + a^2 + a + 1$.

What is the value of $|-15| - |15| + (-15)$?

Simplify: $\frac{x^{a+b} \cdot x^{b+c} \cdot x^{c+a}}{(x^a \cdot x^b \cdot x^c)^2}$.

If $x = \sqrt[3]{2+\sqrt{3}}$, find the value of $x^3 + 1/x^3$.

Find $x$ if $x^{1/12} = 49^{1/24}$.

What is the result of $\frac{1}{2} \times \frac{2}{3} \times \frac{3}{4}$?

If you multiply any rational number by $0$, the result is:

Which of the following is a positive rational number?

Express $0.12$ as a fraction in simplest form.

Which rational number is exactly halfway between $0$ and $0.1$?

Express the result of $0.4 \div 0.25$ as a rational number in simplest form.

Find the difference between $1$ and $\frac{1}{8}$.

Let $x = 0.\overline{ab}$ and $y = 0.\overline{ba}$ be two rational numbers where $a$ and $b$ are distinct non-zero digits. If $x + y = \frac{10}{9}$, what is the maximum possible value of the product $a \times b$?

If the product of two rational numbers is 1, and one of them is $-3\frac{1}{2}$, find the other.

Convert the decimal $0.\overline{321}$ into a rational fraction in lowest terms. What is the sum of the numerator and the denominator?

What is the nature of the number represented by the sum $\sqrt{4} + \sqrt{9}$?

Identify the nature of the result obtained from the expression $(\sqrt{13})^2$.

Determine the nature of the square root of the decimal number $2.25$.

What is the nature of the number represented by $\sqrt{0.4}$?

If $a$ and $b$ are rational numbers such that $\frac{3 + \sqrt{2}}{3 - \sqrt{2}} = a + b\sqrt{2}$, find the value of the expression $a - b$.

The collection of rational and irrational numbers together forms the set of:

Determine the value of $\sqrt[4]{16}$.

If $n$ is a positive integer such that $\sqrt{n+1} + \sqrt{n} = \sqrt{99}$, find the value of $n$.

If $a = 3 + \sqrt{5}$, find the value of $a^2 + \frac{16}{a^2}$.

Simplify: $\sqrt{\frac{x^a}{x^b}}^{a+b} \cdot \sqrt{\frac{x^b}{x^c}}^{b+c} \cdot \sqrt{\frac{x^c}{x^a}}^{c+a}$.

What is the $p/q$ form of $0.\overline{7}$?

Which of these fractions results in a terminating decimal?

The decimal $0.5$ is equal to:

Express $0.\overline{36}$ as a fraction in simplest form.

Arrange the numbers $x = 0.67$, $y = 0.\overline{67}$, and $z = 0.6\overline{7}$ in ascending order.

What is the denominator of $\frac{17}{80}$ when expressed in the form $2^n \times 5^m$?

Find the fraction form of $0.5\overline{8}$.

The decimal $0.abcabc...$ is equivalent to which fraction?

Express $0.12\overline{3}$ as a fraction $\frac{p}{q}$. What is $p$ if $q$ is $900$?

What is the periodicity of the decimal expansion of $\frac{1}{21}$?

The number line contains:

Which of the following is equivalent to $x^m \cdot x^n$?

What is the value of $(1/2)^{-1}$?

Every whole number is a natural number except:

The value of $(0.125)^{1/3}$ is:

Every integer is a rational number. This statement is:

If $2^x \cdot 4^x = 8^2$, what is the value of $x$?

If $x^y = y^x$, and $x = 2y$, find the value of $y$.

The value of $\sqrt{12} + \sqrt{27} - \sqrt{75} + \sqrt{48}$ is equal to:

Find the value of $x$ for which $\sqrt{x+3} + \sqrt{x} = 3$.