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SQUARES AND SQUARE ROOTS A REVIEW

SQUARES AND SQUARE ROOTS A REVIEW. welcome. TO POWERPOINT PRESENTATION. TOPIC. SQUARES AND SQUARE ROOTS. CONTENTS. SQUARES. PERFECT SQUARES. FACTS ABOUT SQUARES. SOME METHODS TO FINDING SQUARES. SOME IMPORTANT PATTERNS. PYTHAGOREAN TRIPLET. SQUARES. 1. 1.

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SQUARES AND SQUARE ROOTS A REVIEW

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  1. SQUARES AND SQUARE ROOTSA REVIEW

  2. welcome TO POWERPOINT PRESENTATION

  3. TOPIC SQUARES AND SQUARE ROOTS

  4. CONTENTS • SQUARES. • PERFECT SQUARES. • FACTS ABOUT SQUARES. • SOME METHODS TO FINDING SQUARES. • SOME IMPORTANT PATTERNS. • PYTHAGOREAN TRIPLET.

  5. SQUARES 1 1 If a whole number is multiplied by itself, the product is called the square of that number. For Examples: 1x 1 = 1 = 12 The square of 1 is 1. 2 x 2 = 4 = 22 The square of 2 is 4 2 2

  6. 3 3 3 x 3 = 9 = 324 x 4 = 16 = 42 4 4

  7. PERFECT SQUARE A natural number ‘x’ is a perfect square, if y2 = x where ‘y’ is natural number. Examples : 16 and 25 are perfect squares, since 16 = 42 25 = 52

  8. FACTS ABOUT SQUARES • A number ending with 2, 3, 7 or 8 is never a perfect square. • The squares of even numbers are even. • The squares of odd numbers are odd. • A number ending with an odd number of zeros is never a perfect square. • The ending digits of a square number is 0, 1, 4, 5, 6 or 9 only. Note : it is not necessary that all numbers ending with digits 0, 1, 4, 5, 6 or 9 are square numbers.

  9. SOME METHODS TO FINDING SQUARES USING THE FORMULA ( a + b )2 = a2 + 2ab + b2 (27)2 = (20 + 7 )2 (20 + 7)2 = (20)2 + 2 x 20x 7 + (7)2 = 400 + 280 + 49 = 729 . FIND (32)2

  10. (a – b )2 = a2 – 2ab + b2 (39)2 = (40 -1)2 (40 – 1)2 = (40)2 – 2 x 40 x 1 + (1)2 = 1600 – 80 + 1 = 1521 . FIND (48)2.

  11. DIAGONAL METHOD FOR SQUARING Example:- Find (72)2 using the diagonal method. SOLUTION:-

  12. ‘FIND (23)2’ • Therefore,(72)2 =5184.

  13. ALTERNATIVE METHOD ALTERNATIVE METHOD

  14. SOME INTERESTING PATTERNS SQUARES ARE SUM OF CONSECUTIVE ODD NUMBERS. EXAMPLES: 1 + 3 = 4 = 22 1 + 3 + 5 = 9 = 32 1+3+5+7 = 16 = 42 1+3+5+7+9 = 25 = 52 1+3+5+7+9+11 = ------- = -------

  15. 2. SQUARES OF NUMBERS ENDING WITH DIGIT 5. (15)2 =1X (1 + 1)X 100 +25 = 1X2X100 + 25 = 200 + 25 = 225 (25)2 = 2X3X100 + 25 = 600 + 25 = 625 (35)2 = (3X4) 25 = 1225 TENS UNITS FIND (45)2

  16. PYTHAGOREAN TRIPLETS If three numbers x, y and z are such that x2 + y2 = z2, then they are called Pythagorean Triplets and they represent the sides of a right triangle. x z y

  17. Examples 3, 4 and 5 form a Pythagorean Triplet. 32 + 42 = 52.( 9 + 16 = 25) (ii) 8, 15 and 17 form a Pythagorean Triplet. 82+152 = 172. (64 +225 = 289)

  18. Find Pythagorean Triplet if one element of a Pythagorean Triplet is given. For any natural number n, (n>1), we have (2n)2 + (n2-1)2 = (n2+1)2. such that 2n, n2-1 and n2+1 are Pythagorean Triplet.

  19. Examples- Write a Pythagorean Triplet whose one member is 12. Since, Pythagorean Triplet are 2n, n2-1 and n2+1. So, 2n = 12, n = 6. n2-1 = (6)2-1 = 36 -1= 35 And n2+1 = (6)2+1= 36+1= 37 Therefore, 12, 35 and 37 are Triplet.

  20. Write a Pythagorean Triplet whose one member is 6.

  21. EVALUATION • EXCEL QUIZ

  22. Thanks

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