at the units place ends in 5. • There are 2n natural numbers between the squares of numbers n and n+1. • A number ending in odd numbers of zeroes is not a perfect square. • The sum of first n odd natural numbers is given by n 2. • Three natural numbers a, b, c are said to form a pythagorean triplet if a2 + b2 = c 2. • For every natural number m > 1, 2m, m 2–1 and m 2 + 1 form a pythagorean triplet. • The square root of a number x is the number whose square is x. Positive square root of a number x is denoted by x. • The cube root of a number x is the number whose cube is x. It is denoted by 3 x . • Square root and cube root are the inverse operations of squares and cubes respectively. • If a perfect square is of n digits, then its square root will have n +1 digit if n is even or digit if n is odd. 2 • Cubes of the numbers ending with the digits 0, 1, 4, 5, 6 and 9 end with digits 0, 1, 4, 5, 6 and 9 respectively. Describe what is meant by a perfect square. Give an example. Explain how many square roots a positive number can have. How are these square roots different? SQUARE ROOTS A square root of a number n is a number m which, when multiplied by itself, equals n. The square roots of 16 are 4 and – 4 because 42 = 16 and (– 4)2 = 16. If m 2 = n, then m is a square root of n. Which type of number has an exact square root? Which type of number has an approximate square root? How can we use perfect squares to estimate a square root, such as 8 ? • Cube of the number ending in 2 ends in 8 and cube root of the number ending in 8 ends in 2. • Cube of the number ending in 3 ends in 7 and cube root of the number ending in 7 ends in 3. In examples 1 to 7, out of given four choices only one is correct. Write the correct answer.
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Five