The problem asks us to classify given numbers into different sets of numbers: - N: Natural numbers - Z: Integers - Q: Rational numbers - I: Irrational numbers - R: Real numbers

1. Problem Description

The problem asks us to classify given numbers into different sets of numbers:

- N: Natural numbers

- Z: Integers

- Q: Rational numbers

- I: Irrational numbers

- R: Real numbers

2. Solution Steps

Let's analyze each number and determine the sets it belongs to:

-3: Negative integer.

* Z: Yes (Integers include negative and positive whole numbers and zero)

* Q: Yes (Any integer can be written as a fraction, e.g., -3/1)

* R: Yes (All rational numbers are real numbers)

$\frac{12}{4}$: Simplify to

3. * N: Yes (Natural numbers start from 1: 1, 2, 3...)

* Z: Yes (3 is an integer)

* Q: Yes (3 can be written as 3/1)

* R: Yes (All rational numbers are real numbers)

$-\pi$: Pi is an irrational number, so $-pi$ is also irrational.

* I: Yes

* R: Yes (Irrational numbers are real numbers)

$-\frac{15}{3}$: Simplify to -

5. * Z: Yes (Integers)

* Q: Yes (Any integer can be written as a fraction, e.g., -5/1)

* R: Yes (All rational numbers are real numbers)

1. 2: Decimal. $1.2 = \frac{12}{10} = \frac{6}{5}$

* Q: Yes (Can be expressed as a fraction)

* R: Yes (All rational numbers are real numbers)

$\frac{3}{2}$: Fraction.

* Q: Yes (Fraction)

* R: Yes (All rational numbers are real numbers)

$-\frac{1}{5}$: Fraction.

* Q: Yes (Fraction)

* R: Yes (All rational numbers are real numbers)

$\sqrt{7}$: Square root of a non-perfect square.

* I: Yes (Cannot be expressed as a fraction of two integers)

* R: Yes (Irrational numbers are real numbers)

1. 136666...: Repeating decimal.

* Q: Yes (Repeating decimals can be expressed as fractions)

* R: Yes (All rational numbers are real numbers)

$-\sqrt{36}$: Simplify to -

6. * Z: Yes (Integers)

* Q: Yes (Any integer can be written as a fraction, e.g., -6/1)

* R: Yes (All rational numbers are real numbers)

$-\sqrt{11}$: Square root of a non-perfect square.

* I: Yes (Cannot be expressed as a fraction of two integers)

* R: Yes (Irrational numbers are real numbers)

3. Final Answer

Here's the classification of each number:

-3: Z, Q, R

12/4: N, Z, Q, R

-π: I, R

-15/3: Z, Q, R

1.2: Q, R

3/2: Q, R

-1/5: Q, R

√7: I, R

1.136666...: Q, R

-√36: Z, Q, R

-√11: I, R