Squares and Square Roots: Concepts and Applications
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SQUARES
&
SQUARE ROOTS
Module 2/4
Squares and Square Roots
Class - VIII
Prepared by – Bashuki Nath, AECS, Anupuram
F
INDING
THE
S
QUARE
OF
A
N
UMBER
Module 2/4
Squares and Square Roots
Class - VIII
Prepared by – Bashuki Nath, AECS, Anupuram
Squares of small numbers like 1, 2, 3, 4,
5, 6, 7, ... etc. are easy to find.
4
2
= 4
4 = 16
N
OW
WE
WILL
FIND
THE
SQUARE
OF
TWO
DIGIT
NUMBERS
SO
QUICKLY
Module 2/4
Squares and Square Roots
Class - VIII
Prepared by – Bashuki Nath, AECS, Anupuram
So 12
2
= 144
F
INDING
THE
S
QUARE
OF
A
N
UMBER
ENDING
5
Module 2/4
Squares and Square Roots
Class - VIII
Prepared by – Bashuki Nath, AECS, Anupuram
(a5)
2
= a(a + 1) hundred + 25
7
5
2
= (
7
× 8) hundreds + 25 = 5600 + 25 = 5625
P
YTHAGOREAN
TRIPLETS
Module 2/4
Squares and Square Roots
Class - VIII
Prepared by – Bashuki Nath, AECS, Anupuram
The set of three numbers are called Pythagorean
triplet if the sum of the squares of smaller numbers is
equal to the square of largest number
P
YTHAGOREAN
TRIPLETS
Module 2/4
Squares and Square Roots
Class - VIII
Prepared by – Bashuki Nath, AECS, Anupuram
General form for Pythagorean
triplet is 2m, m
2
– 1 and m
2
+ 1
P
YTHAGOREAN
TRIPLETS
Module 2/4
Squares and Square Roots
Class - VIII
Prepared by – Bashuki Nath, AECS, Anupuram
All Pythagorean triplets may not be
obtained using general form. For
example another triplet 5, 12, 13 also
has 12 as a member.
P
YTHAGOREAN
TRIPLETS
Module 2/4
Squares and Square Roots
Class - VIII
Prepared by – Bashuki Nath, AECS, Anupuram
Some Pythagorean triplets are
3, 4, 5
5, 12, 13
7, 24, 25
8, 15, 17
6, 8, 10
20, 21, 29
20, 99, 101
9, 40, 41
P
YTHAGOREAN
TRIPLETS
Module 2/4
Squares and Square Roots
Class - VIII
Prepared by – Bashuki Nath, AECS, Anupuram
If you multiply any Pythagorean triplet with any
constant, the resulting set will again the
Pythagorean triplet.
(3, 4, 5) is a Pythagorean triplet
(3, 4, 5)
2 = (6, 8, 10) is also a Pythagorean triplet
(3, 4, 5)
3 = (9, 12, 15) is also a Pythagorean triplet
(3, 4, 5)
7 = (21, 28, 35) is also a Pythagorean triplet
Module 2/4
Squares and Square Roots
Class - VIII
Prepared by – Bashuki Nath, AECS, Anupuram
THANK YOU
Delve into the world of squares and square roots in this comprehensive module for Class VIII. Discover how to find the squares of numbers efficiently, explore Pythagorean triplets, and understand their general forms. Uncover the beauty of mathematical relationships and patterns in this engaging learning resource.
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Presentation Transcript
Squares and Square Roots Class - VIII Module 2/4 SQUARES & SQUARE ROOTS Prepared by Bashuki Nath, AECS, Anupuram
Squares and Square Roots Class - VIII Module 2/4 FINDINGTHE SQUARE OFA NUMBER Squares of small numbers like 1, 2, 3, 4, 5, 6, 7, ... etc. are easy to find. 42 = 4 4 = 16 Prepared by Bashuki Nath, AECS, Anupuram
Squares and Square Roots Class - VIII Module 2/4 NOWWEWILLFINDTHESQUAREOF TWODIGITNUMBERSSOQUICKLY So 122 = 144 Prepared by Bashuki Nath, AECS, Anupuram
Squares and Square Roots Class - VIII Module 2/4 FINDINGTHE SQUARE OFA NUMBERENDING 5 (a5)2 = a(a + 1) hundred + 25 752 = (7 8) hundreds + 25 = 5600 + 25 = 5625 Prepared by Bashuki Nath, AECS, Anupuram
Squares and Square Roots Class - VIII Module 2/4 PYTHAGOREAN TRIPLETS The set of three numbers are called Pythagorean triplet if the sum of the squares of smaller numbers is equal to the square of largest number Prepared by Bashuki Nath, AECS, Anupuram
Squares and Square Roots Class - VIII Module 2/4 PYTHAGOREAN TRIPLETS General form for Pythagorean triplet is 2m, m2 1 and m2 + 1 Prepared by Bashuki Nath, AECS, Anupuram
Squares and Square Roots Class - VIII Module 2/4 PYTHAGOREAN TRIPLETS All Pythagorean triplets may not be obtained using general form. For example another triplet 5, 12, 13 also has 12 as a member. Prepared by Bashuki Nath, AECS, Anupuram
Squares and Square Roots Class - VIII Module 2/4 PYTHAGOREAN TRIPLETS Some Pythagorean triplets are 6, 8, 10 20, 21, 29 20, 99, 101 9, 40, 41 3, 4, 5 5, 12, 13 7, 24, 25 8, 15, 17 Prepared by Bashuki Nath, AECS, Anupuram
Squares and Square Roots Class - VIII Module 2/4 PYTHAGOREAN TRIPLETS If you multiply any Pythagorean triplet with any constant, the resulting set will again the Pythagorean triplet. (3, 4, 5) is a Pythagorean triplet (3, 4, 5) 2 = (6, 8, 10) is also a Pythagorean triplet (3, 4, 5) 3 = (9, 12, 15) is also a Pythagorean triplet (3, 4, 5) 7 = (21, 28, 35) is also a Pythagorean triplet Prepared by Bashuki Nath, AECS, Anupuram
Squares and Square Roots Class - VIII Module 2/4 THANK YOU Prepared by Bashuki Nath, AECS, Anupuram
