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Properties of Square - Based on Pattern

Square and Square Root I - Concepts

Perfect Square

Square of Number 1-50

Square Root Using Prime Factorization

General Properties of Squares

Properties of Square - Based on Ending Digits

Properties of Square - Unit Digit of Square

Properties of Square - Difference of Consecutive Numbers

Pythagorean Triplet

Number Between Square Numbers

Properties of Square - Based on Pattern

Class - Navodaya Entrance 9th Subjects

Concept Explanation

Properties of Square - Based on Pattern

A pattern refers to a series or sequence which repeats. There are two major kinds of math patterns. They are number patterns or sequences of numbers. These are arranged as per a rule or rules or a formula. The other type we have are shape patterns that are tagged by making use of letters in a definite shape and the way that they repeat.

Some interesting patterns of square numbers :

Pattern 1:The sum of two consecutive triangular numbers is a square number .

Numbers whose dot patterns can be arranged as triangles are known as triangular numbers.1,3,6,10,15,21,... are triangular numbers.This fact can be observed by the following pattern

$1=1^{2}$

$1+3=4=2^{2}$

$3+6=9=3^{2}$

$6+10=16=4^{2}$

$10+15=25=5^{2}$

$15+21=36=6^{2}$ etc.

Also n^th triangular number is given by $frac{n(n+1)}{2}$

Pattern 2: If 1 is added to the product of two consecutive odd natural numbers,it is equal to the square of the only even natural number between them.

This fact can be observed by the following pattern

$1times3+1=4=2^{2}$

$3times5+1=16=4^{2}$

$5times7+1=36=6^{2}$

$7times9+1=64=8^{2}$

$9times11+1=100=(10)^{2}$ etc.

In general, $(2n-1)times(2n+1)+1=4n^{2}=(2n)^{2}$

Pattern 3: If 1 is added to the product of two consecutive even natural numbers,it is equal to the square of the only odd natural number between them.

This fact can be observed by the following pattern

$2times4+1=9=3^{2}$

$4times6+1=25=5^{2}$

$6times8+1=49=7^{2}$

$8times10+1=81=9^{2}$

$10times12+1=121=(11)^{2}$ etc.

In general: $2ntimes(2n+2)+1=4n^{2}+4n+1=(2n+1)^{2}$

Pattern 4:The square of any odd natural number other than 1 can be expressed as the sum of two consecutive natural numbers.

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Sample Questions

(More Questions for each concept available in Login)

Question : 1

Which of the following statements are false 1. The number of digits in a square number is even. 2. The square of a prime number is prime 3. No square number is negative. 4. The sum of two square numbers is a square number.
A. 1,2,3	B. 1,3	C. 1,2,4	D. 2,4
Right Option : C
View Explanation

Question : 2

Observe the following pattern $2^{2}-1^{2}=2+1$ $3^{2}-2^{2}=3+2$ $4^{2}-3^{2}=4+3$ $5^{2}-4^{2}=5+4$ and find the value of $(100)^{2}-(99)^{2}$
A. 99	B. 1	C. 199	D. 299
Right Option : C
View Explanation

Question : 3

Express $(21)^{2}$ as the sum of two consecutive natural numbers.
A. 220+221	B. 100+341	C. 400+41	D. none of these
Right Option : A
View Explanation

Chapters

Lines and Angles I

Square and Square Root II

Cube and Cube Roots

Linear Equations in One Variable I

Linear Equations in One Variable II

Square and Square Root I

Triangles and its Properties I

Triangles and its Properties II

Partnership and Mixture

Time, Speed and Distance

Pipe And Cistern

Problems On Trains

Problems On Boats And Stream

Mensuration I

Rational Numbers II

Rational Numbers I

Exponents and Power II

Exponents and Power I

Direct and Inverse Variation II

Direct and Inverse Variation I

Data Handling

Factorisation

Algebraic Identities

Algebraic Expressions

Comparing Quantities III

Comparing Quantities II

Comparing Quantities I

Content / Category

IMO-Mathematics Olympiad

Central Government Service

ISO - Science Olympiads

State Government Services

Banking And Insurance

Railways & Metro Services

MBA Entrance

Law Entrance

English Proficiency

Reasoning Proficiency

Computer Proficiency

Navodaya Entrance 6th & 9th

Sainik School Entrance

Andhra Bank

Class / Course

Navodaya Entrance 6th

Navodaya Entrance 9th

Why ABHYAS?

Self Learning

Course Benefits

Our Areas of Expertise

IMO-Mathematics Olympiad

Central Government Service

ISO - Science Olympiads

State Government Services

Banking And Insurance

Railways & Metro Services

MBA Entrance

Law Entrance

English Proficiency

Reasoning Proficiency

Computer Proficiency

Navodaya Entrance 6th & 9th

Sainik School Entrance

Andhra Bank

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Attention !!!!!

Properties of Square - Based on Pattern

Properties of Square - Based on Pattern

Some interesting patterns of square numbers :

Pattern 1:The sum of two consecutive triangular numbers is a square number .

Pattern 2: If 1 is added to the product of two consecutive odd natural numbers,it is equal to the square of the only even natural number between them.

Pattern 3: If 1 is added to the product of two consecutive even natural numbers,it is equal to the square of the only odd natural number between them.

Pattern 4:The square of any odd natural number other than 1 can be expressed as the sum of two consecutive natural numbers.

Students / Parents Reviews [10]

Manish Kumar

Prisha Gupta

Shreya Shrivastava

Archit Segal

Aman Kumar Shrivastava

Hiya Gupta

Om Umang

Cheshta

Barkha Arora

Shivam Rana