1) Show that 3√ 2 is irrational.
2) Prove that 3 + 2 √5 is irrational.
3) A sweet seller has 420 kaju barfis and 130 badam barfis. She wants to stack them in such a way that each stack has the same number, and they take up the least area of the tray. What is the maximum number of barfis that can be placed in each stack for this purpose?
4) Use Euclid’s division algorithm to find the HCF of : (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255
5) Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.
6) An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march? Sol. Hints: Find the HCF of 616 and 32
7) Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m. [Hint : Let x be any positive integer then it is of the form 3q, 3q + 1 or 3q + 2. Now square each of these and show that they can be rewritten in the form 3m or 3m + 1.]
8) Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.
9) Consider the numbers 4n, where n is a natural number. Check whether there is any value of n for which 4n ends with the digit zero.
10) Find the LCM and HCF of 6 and 20 by the prime factorization method.
11) Find the HCF of 96 and 404 by the prime factorization method. Hence, find their LCM.
12) Find the HCF and LCM of 6, 72 and 120, using the prime factorization method.
13) Find the value of y if the HCF of 210 and 55 is expressible in the form 210 x 5 + 55y
14) Prove that no number of the type 4K + 2 can be a perfect square.
15) Express each number as a product of its prime factors:
3) A sweet seller has 420 kaju barfis and 130 badam barfis. She wants to stack them in such a way that each stack has the same number, and they take up the least area of the tray. What is the maximum number of barfis that can be placed in each stack for this purpose?
4) Use Euclid’s division algorithm to find the HCF of : (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255
5) Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.
6) An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march? Sol. Hints: Find the HCF of 616 and 32
7) Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m. [Hint : Let x be any positive integer then it is of the form 3q, 3q + 1 or 3q + 2. Now square each of these and show that they can be rewritten in the form 3m or 3m + 1.]
8) Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.
9) Consider the numbers 4n, where n is a natural number. Check whether there is any value of n for which 4n ends with the digit zero.
10) Find the LCM and HCF of 6 and 20 by the prime factorization method.
11) Find the HCF of 96 and 404 by the prime factorization method. Hence, find their LCM.
12) Find the HCF and LCM of 6, 72 and 120, using the prime factorization method.
13) Find the value of y if the HCF of 210 and 55 is expressible in the form 210 x 5 + 55y
14) Prove that no number of the type 4K + 2 can be a perfect square.
15) Express each number as a product of its prime factors:
(i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429
You may also see
CBSE :10th Real Numbers Extra score Test paper
You may also see
CBSE :10th Real Numbers Extra score Test paper
I am here to discuss about the rational and irrational. A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers.What are Rational and Irrational Numbers
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