Math questions: Bunches?!?

Question

Write all names that apply to each number(real,irrational,rational)

#1. √12
#2. 0.15
#3. √1600
#4.- √144

#5. Give an example of an irrational number that is less than -5

#6. Find a real number bewteen 5 and √36

Answer 1

1). √12 = 3.464 so, it is the rational - real number

2). 0.15 it is the rational - real number

3). √1600 = √(40)² = 40 so, it is the rational - real number

4). - √144 = - √(12)² = -12  so, it is the rational - real numbers

5). The negative square root of 6 it is irrational and not real number.

6). √36 = ± 6

If (+ 6) then (5 + 6)/2 = 11/2 = 5.5

If (- 6) then (5 - 6)/2 = (-1/2) = -0.5

A real number bewteen 5 and √36 is 5.5

So basically rational numbers are numbers that can be written as a fraction and irrational numbers are numbers can't be written as a fraction.

Comments

Real numbers :  Real numbers are numbers that can be found on the number line. This includes both the rational and irrational numbers.

By real number we mean, loosely, a number that we can conceive of in this world, one with no square roots of negative numbers (such a number is called complex.)

Examples :  - 5, 4/3, √2, π, and 8.636.

Irrational numbers : Irrational numbers are numbers that can be written as decimals but not as fractions.

An irrational number is any real number that is not rational.

Ex : √2 is an irrational number because it can't be written as a ratio of two integers.

Rational numbers : A rational number is any number that can be written as a ratio of two integers (hence the name!). In other words, a number is rational if we can write it as a fraction where the numerator and denominator are both integers.

The term "rational" comes from the word "ratio," because the rational numbers are the ones that can be written in the ratio form p/q where

p and q are integers. Irrational, then, just means all the numbers that aren't rational.

Every integer is a rational number, since each integer

n can be written in the form n/1.

Ex :

5 = 5/1 and thus 5 is a rational number. However, numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers.

So the set of all rational numbers will contain the numbers 4/5, -8, 1.75 (which is 7/4), -97/3, and so on.

 

1. √12 = 3.464 = irrational number.
2. 0.15 = 15/100 = 3/20 = rational real number.
3. √1600 = 40 = rational real number.
4. - √144 = - 12 = rational real number.
5. Just pick √2 and multiply by - 5 → - 5(√2) = - 7.07.
6. √36 = ± 6

   If (+ 6) then (5 + 6)/2 = 11/2 = 5.5

   If (- 6) then (5 - 6)/2 = (-1/2) = -0.5

   A real number bewteen 5 and √36 is 5.5.