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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 - 8th DAV 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

Express $(13)^{2}$ as the sum of two consecutive natural numbers.
A. 168+1	B. 84+85	C. 100+69	D. none of these
Right Option : B
View Explanation

Question : 2

Using suitable pattern compute $frac{(666666)^{2}}{12345654321}$
A. 36	B. 32	C. 38	D. 46
Right Option : A
View Explanation

Question : 3

Observe the 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 $(111)^{2}-(109)^{2}$
A. 420	B. 430	C. 340	D. 440
Right Option : D
View Explanation

Chapters

Exponents And Radicals II

Direct and Inverse Variation III

Construction of Quadriletrals

Understanding Quadriletrals II

Understanding Quadriletrals I

Linear Equations in One Variable II

Linear Equations in One Variable I

Cube and Cube Roots

Square and Square Root II

Square and Square Root I

Mensuration I

Exponents And Radicals I

Direct and Inverse Variation II

Direct and Inverse Variation I

Statistics and Probability I

Statistics and Probability II

Factorisation

Algebraic Identities

Polynomial

Simple and Compound Interest

Profit Loss and Discount

Percentages

Introduction to Graphs

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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]

Shivam Rana

Prisha Gupta

Eshan Arora

Ayan Ghosh

Om Umang

Archit Segal

Barkha Arora

Cheshta

Yatharthi Sharma

Aman Kumar Shrivastava