Mathematic Worksheet - 1
TOPIC: Real Numbers
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REAL NUMBERS: Number which can represent its actual physical quantities in a meaningful way is called as real number.
PRIME NUMBERS: All the numbers that have one and itself only as their factor is called as prime number.
COMPOSITE NUMBER: All natural number which are not prime are composite numbers.
EUCLID’S DIVISION LEMMA
Let a and b be any two positive integer. Then, there exists unique integers q and r such that a = bq + r, where 0 ≤ r ≤ b. If b|a, then r = 0.
FUNDAMENTAL THEOREM OF ARITHEMATIC
Every composite number can be expressed as a product of primes and this factorization is unique , except for the order in which the prime factors occurs.
1) Prove that √2 + √3.
2) An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are in same in numbers of columns. What is the maximum no. of columns in which they can march?
3) There is a circular path around a sports field. Sonia takes 15 minutes to drive a round of the field, while Ravi takes 12 minutes for the same. Suppose they start at the same point and the same time and go in the same direction. After how many minutes will they meet again at the starting point?
4) Write rational numbers between √2 and √3..
5) Use EUCLID’S DIVISION LEMMA to shoe that the square of any positive number is either of the form 3m or 3m+1 for some integer.
6) Write whether (2√45+3√20)/(2√5) on simplification gives a rational or an irrational number.
2) 8 columns
3) 36 minutes
6) 6 (rational number)