Class 8 Maths NotesClass 8 Maths NotesTue, 18 Jun 2019 05:43:37 +0000Tue, 18 Jun 2019 05:43:37 +0000CBSE Labs
http://www.cbselabs.com/forums/class-8-maths-notes.14/
If 1 is added to the product of two consecutive even natural numbersFri, 28 Jan 2011 10:32:43 +0000
http://www.cbselabs.com/threads/if-1-is-added-to-the-product-of-two-consecutive-even-natural-numbers.13/
http://www.cbselabs.com/threads/if-1-is-added-to-the-product-of-two-consecutive-even-natural-numbers.13/sastrysastry
Explanation: We have,
2x4÷1=9=32
4x6÷1=25=52
6 x8 +1= 49 = 72
8x10÷1=81=92
10x12÷1=121=112 etc.

In general,

2nx(2n +2) +1 =4n2 +4n +1 =(2n +1)2.

ILLUSTRATIVE EXAMPLES

Example 1 ‘The following numbes are not perfect squares. Give reason.
(i) 1057 ii)-2’3453 (iii) 7928 (iv) 222222

Solution We know that the natural...

If 1 is added to the product of two consecutive even natural numbers]]>If 1 is added to the product of two consecutive odd natural numbersFri, 28 Jan 2011 10:31:32 +0000
http://www.cbselabs.com/threads/if-1-is-added-to-the-product-of-two-consecutive-odd-natural-numbers.12/
http://www.cbselabs.com/threads/if-1-is-added-to-the-product-of-two-consecutive-odd-natural-numbers.12/sastrysastry
Explanation: We have,
1x3+1=4=22
3x5+1=16=42
5x7+1=36=62
7x9÷1=64=82
9x11÷1=100=102 etc.

In general,
(2n— 1)x(2n ÷1)÷1 =4n2 =(2n)2]]>the difference of squares of two consecutive natural numbers is equal to their sumFri, 28 Jan 2011 10:29:33 +0000
http://www.cbselabs.com/threads/the-difference-of-squares-of-two-consecutive-natural-numbers-is-equal-to-their-sum.11/
http://www.cbselabs.com/threads/the-difference-of-squares-of-two-consecutive-natural-numbers-is-equal-to-their-sum.11/sastrysastry
(n+1)^2 - n^2 =(n+1)+n
the difference of squares of two consecutive natural numbers is equal to their sum

Proof: For any natural number n, we have
(n+1)^2—n^2 =(n+1+n)(n+1—n)
= (n +1+ n)

The square of a natural number n is equal to the sum of first n odd natural numbers.

1^2 = 1 = Sum of first 1 odd natural number;...

the difference of squares of two consecutive natural numbers is equal to their sum]]>PROPERTIES AND PATTERNS OF SOME SQUARE NUMBERS - CASE 3Fri, 28 Jan 2011 10:19:33 +0000
http://www.cbselabs.com/threads/properties-and-patterns-of-some-square-numbers-case-3.10/
http://www.cbselabs.com/threads/properties-and-patterns-of-some-square-numbers-case-3.10/sastrysastry
In this case,
p is even
zz p contains 2 as a factor
= p2 contains 22(= 4) as a factor
q is odd
= qisodd

2q2 contains 2 as the only even factor.

Thus, p2 contains 4 as the smallest even factor and 2q2 contains only 2 as the even factor.
So, p2 = 2q2 is not possible.
Thus, p2 = 2q2 is not possible when p is even and q is odd.]]>PROPERTIES AND PATTERNS OF SOME SQUARE NUMBERS case -2Fri, 28 Jan 2011 10:18:52 +0000
http://www.cbselabs.com/threads/properties-and-patterns-of-some-square-numbers-case-2.9/
http://www.cbselabs.com/threads/properties-and-patterns-of-some-square-numbers-case-2.9/sastrysastry
Since the square of an odd natural number is an odd natural number and that of an even natural number is even. Therefore,

p is odd and q is even
= p2 is odd and q2 is even
= p2 is odd and 2q2 is even
= p2 = 2q is not possible.

Thus, p2 = 2q2 is not possible when p is odd and q is even.]]>PROPERTIES AND PATTERNS OF SOME SQUARE NUMBERS case - 1Fri, 28 Jan 2011 10:17:35 +0000
http://www.cbselabs.com/threads/properties-and-patterns-of-some-square-numbers-case-1.8/
http://www.cbselabs.com/threads/properties-and-patterns-of-some-square-numbers-case-1.8/sastrysastry
Since the square of an odd natural number is odd and that of an even natural number is
even.

Therefore p and q are odd
= p^2 and q^2 are odd
= p^2 is odd and 2q^2 is even
= p^2 = 2q^2 is not possible.

Thus, p2 = 2q2 is not possible when p and q both are odd natural numbers.]]>Squares and Square rootsSat, 22 Jan 2011 13:06:05 +0000
http://www.cbselabs.com/threads/squares-and-square-roots.5/
http://www.cbselabs.com/threads/squares-and-square-roots.5/cbselabscbselabsSquare: If a number is multiplied by itself, the product so obtained is called the square of that number.

For Example: 3X3 = 3^2 = 9 We say that 9 is the square of 3. 16X16 = 16^2 = 256 We say that 256 is the square of 16.

A square of a number is a number raised to the power 2.

Properties of a square numbers:
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[url='http://www.cbselabs.com/threads/squares-and-square-roots.5/']Squares and Square roots[/url]]]>