MATHEMATICS Textbook for Class VIII>Squares and Square Roots>Some More Interesting Patterns

Some More Interesting Patterns

Author:Madhya Pradesh Board

8th Madhya Pradesh Board

IMPORTANT

Some More Interesting Patterns: Overview

This topic brings interesting patterns like adding triangular numbers, numbers between square numbers, etc. If a natural number cannot be expressed as a sum of successive odd natural numbers starting with 1, then it is not a perfect square.

Important Questions on Some More Interesting Patterns

MEDIUM

IMPORTANT

MATHEMATICS Textbook for Class VIII>Squares and Square Roots>Some More Interesting Patterns> Q 1

Using the given pattern, find the missing numbers.
$1^{2} + 2^{2} + 2^{2} = 3^{2}$
$2^{2} + 3^{2} + 6^{2} = 7^{2}$
$3^{2} + 4^{2} + 12^{2} = 13^{2}$
$4^{2} + 5^{2} + {__}_{}^{2} = 21^{2}$
$5^{2} + {__}_{}^{2} + 30^{2} = 31^{2}$
$6^{2} + 7^{2} + {__}_{}^{2} = {__}_{}^{2}$

HARD

IMPORTANT

MATHEMATICS Textbook for Class VIII>Squares and Square Roots>Some More Interesting Patterns> Q 2

Observe the following pattern and supply the missing number.
   $11^{2} = 121$
$101^{2} = 10201$
   $10101^{2} = 102030201$
   $1010101^{2} = . \dots \dots . . . . . . .$
$. . . . . . . . . . . \dots^{2} = 10203040504030201$

MEDIUM

IMPORTANT

MATHEMATICS Textbook for Class VIII>Squares and Square Roots>Some More Interesting Patterns> Q 3

Observe the following pattern and find the missing digits.
$11^{2} = 121$
$101^{2} = 10201$
$1001^{2} = 1002001$
$100001^{2} = 1 . . . . . . . . 2 . . . . . . . . . 1$
$10000001^{2} = \dots \dots \dots . . . . . . . .$