Step 1a

The given number is \$5/6\$.

Explanation: Here we write the given data.

Step 1b

In this case, the number \$ (5/6) \$ is a rational number because it can be expressed as a fraction of two integers where the denominator is not zero.

Explanation: Identify the appropriate classification(s) based on the properties of the number.

Step 2a

The given number is \$\sqrt 3\$.

Explanation: Here we write the given data.

Step 2b

Real numbers include all rational and irrational numbers. Since \$ \sqrt(3) \$ is a non-negative, non-repeating, non-terminating decimal, it is a real number.

Explanation: Determining whether a given value is a real number or not.

Step 2c

Assume \$\sqrt(3) \$ is rational.
Square both sides of \$\sqrt(3) = q/p \$ to obtain 3 = \$ p^2 / q^2 \$.
Deduce that p and q must both be divisible by 3, leading to a contradiction.

Explanation: Verifying it as an irrational number. Therefore, \$ \sqrt(3) \$ is both a real number and an irrational number.

Step 3a

The given number is \$-3\$

Explanation: Here we write the given data.

Step 3b

Since −3 represents a point on the number line and is a valid numerical value, it is a real number.

Explanation: Identifying it as a Real Number.

Step 3c

An integer is a whole number that can be positive, negative, or zero. For instance, -3 is a negative integer. Therefore, −3 is both a real number and an integer.

Explanation: Here we Identify it as an Integer and a real number.