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Squares and Square Roots - NCERT

Squares AND Square Roots IntroductionYou know that the area of a Square = side side (where side means the length ofa side ). Study the following of a Square (in cm)Area of the Square (in cm2)11 1 = 1 = 1222 2 = 4 = 2233 3 = 9 = 3255 5 = 25 = 5288 8 = 64 = 82aa a = a2 What is special about the numbers 4, 9, 25, 64 and other such numbers?Since, 4 can be expressed as 2 2 = 22, 9 can be expressed as 3 3 = 32, all suchnumbers can be expressed as the product of the number with numbers like 1, 4, 9, 16, 25, .. are known as Square general, if a natural number m can be expressed as n2, where n is also a naturalnumber, then m is a Square number. Is 32 a Square number?We know that 52 = 25 and 62 = 36. If 32 is a Square number, it must be the Square ofa natural number between 5 and 6.

(i) 38 – 1 = 37 (ii) 37 – 3 = 34 (iii) 34 – 5 = 29 (iv) 29 – 7 = 22 (v) 22 – 9 = 13 (vi) 13 – 11 = 2 (vii) 2 – 13 = – 11 This shows that we are not able to express 38 as the sum of consecutive odd numbers starting with 1. Also, 38 is not a perfect square. So we …

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