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Thought-Process to Discover Knowledge

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nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

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trek,

jogger,

exercise.

User Guide

nub is the simple explanation of the concept.

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User Guide

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User Guide

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exercise provides practice problems to become fluent in the concepts.

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge.

summary of this topic

Introduction to Complex Numbers

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Irrational Number Representation

»  irrational numbers
→  solutions of algebraic equations in real line
→  eg: sqrt(2) is one solution of x^2=2

»  irrational numbers are represented as numerical expressions
→  eg: 3+4 root(3)(5) is one solution of ((x-3)/4)^3 = 5

Irrational Number Notation

plain and simple summary

nub

plain and simple summary

nub

dummy

Irrational numbers are represented as numerical expressions or with a symbol.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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This page reviews the representation of irrational numbers. The complex number notation is very similar to the representation of irrational numbers -- both are given as numerical expressions.

Keep tapping on the content to continue learning.
Starting on learning "Irrational Number Notation". ;; This page reviews the representation of irrational numbers. The complex number notation is very similar to the representation of irrational numbers -- both are given as numerical expressions.

Irrational numbers are 'numbers that cannot be represented as p/q and are on the number line.
The equation x^2 = 2 has the solutions in irrational numbers. Which one in the following is the exact solution?

• +-1.4
• +-1.41
• +-1.414
• none of the above is the exact solution

The answer is 'None of these is the exact solution'.

What is the value of x in x^2=2?

• +-sqrt(2)
• the solution is given as a numerical expression
• both the above

The answer is 'Both the above'. sqrt(2) is a numerical expression involving a square root symbol.

What is the solution to (x-1)^2=2?

• +-sqrt(2)+1
• the solution is given as a numerical expression
• both the above

The answer is 'Both the above'. sqrt(2)+1 is a numerical expression involving a square root symbol and an addition.

What is the ratio of circumference to diameter of a circle? Find the exact value in the following.

• 22/7
• 3.14
• pi

The answer is 'pi'. The number is represented with a symbol or a letter.

is pi a rational number?

• No, pi is an irrational number
• yes, pi is a rational number

The answer is 'No, pi is an irrational number'. This particular irrational number is represented with a letter pi.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Representation of Irrational Numbers : Irrational numbers are represented with numerical expressions (eg: root(3)(4)+3) or with symbols (eg: pi, e)

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Is e (a constant, that is base of natural logarithm) a rational number?

• No. e is an irrational number
• Yes. e is a rational number

The answer is 'No. e is an irrational number'

your progress details

Progress

About you

Progress

Irrational numbers are 'numbers that cannot be represented as p by q and are on the number line'. ;; The equation x squared = 2 has the solutions in irrational numbers. Which one in the following is the exact solution?
plus;minus;1
plus or minus 1 point 4
point;4
plus or minus 1 point 4 one
4 1 4
plus or minus 1 point 4 one four
none;above;exact;solution
none of the above is the exact solution
The answer is 'None of these is the exact solution'.
What is the value of x in x squared equals 2?
plus;minus;square;root;2
plus or minus square root of 2
solution;numerical;expression
the solution is given as a numerical expression
both;above
both the above
The answer is 'Both the above'. ;; square root of 2 is a numerical expression involving a square root symbol.
what is the solution to x minus 1 squared equals 2?
plus;minus;square;root
plus or minus square root of 2 plus 1
solution;numerical;expression
the solution is given as a numerical expression
both;above
both the above
The answer is 'Both the above'. Square root of 2 plus 1 is a numerical expression involving a square root symbol and an addition.
What is the ratio of circumference to diameter of a circle? Find the exact value in the following.
22;7;by
22 by 7
3;point;1;4
3 point one 4
pi;pie
pi
The answer is ' pi '. The number is represented with a symbol or a letter.
is pi a rational number?
no;irrational
No, pi is an irrational number
yes;rational
yes, pi is a rational number
The answer is 'No, pi is an irrational number'. This particular irrational number is represented with a letter pi .
Irrational numbers are represented as numerical expressions or with a symbol.
Representation of Irrational Numbers : Irrational numbers are represented with numerical expressions. ;; for example third root of 4 plus 3 ;; or with symbols ;; for example pi and e.
Is e ;; a constant that is base of natural logarithm ;; a rational number?
no;irrational
No. e is an irrational number
yes;s;rational
Yes. e is a rational number
The answer is 'No. e is an irrational number'

we are not perfect yet...
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