Using the method of successive subtraction (numbers: 1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397,…) examine whether or not the following numbers are perfect cubes: 130      (ii) 345      (iii) 792                (iv)  1331

Find the cube roots of the following numbers by successive subtraction of numbers: 1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397,… (i) 64 (ii) 512 (iii) 1728

using the method of successive subtraction examine whether or not the following numbers are perfect cube (i) 130 (ii) 345 (iii) 792 (iv) 1331 Find the smallest number that must be subtracted from those of the numbers in above question which are not perfect cubes, to make them perfect cubes. What are the corresponding cube roots?

Examine, whether the following numbers are rational or irrational: (i) 0. 3796 (ii) 7. 478478....... (iii) 1.101001000100001

Find the cube root of each of the following rational numbers: 0.001728 (ii) 0.003375 (iii) 0.001 (iv) 1.331

Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication: (I)25 (ii) 37 (iii) 54 (iv)71 (v) 96

Taking the set of natural numbers as the universal set, write down the complements of the following sets: (i) {x : x is an even natural number} (ii) { x : x is an odd natural number } (iii) {x : x is a positive multiple of 3} (iv) { x : x is a prime number } (v) {x : x is a natural number divisible by 3 and 5} (vi) { x : x is a perfect square } (vii) { x : x is a perfect cube} (viii) { x : x + 5 = 8 }(ix) { x : 2x + 5 = 9} (x) { x : x ≥ 7 }(xi) { x : x ∈ N and 2x + 1 > 10 }

Write each of the following phrases using numbers, literals and the basic operation of subtraction: (i) 5 less than a literal xdot (ii) Decreases x\ by 7. (iii) Subtract 4 from xdot (iv) x less than the sum of y\ a n d\ 7 (v) Decrease the sum of x\ a n d\ y by z (vi) a is diminished by 2 (vii) a less than 4.

Examine whether the following statements are true or false: (i) { a, b } ⊄ { b , c, a } (ii) { a , e } ⊂ { x : x is a vowel in the English alphabet} (iii) { 1, 2, 3 } ⊂ { 1, 3, 5 } (iv) { a }⊂ { a, b, c } (v) { a }∈ { a , b, c } (vi) { x : x is an even natural number less than 6} ⊂ { x : x is a natural number which divides 36}

Which of the two rational numbers is greater in each of the following pairs? (i) 3/-7 or 1/7 , (ii) 11/(-18) or -5/18 , (iii) 7/10 or -9/10 (iv) 0 or -3/4 , (v) 1/12 or 0, (vi) 18/(-19) or 0 (vii) 7/8 or 11/16 , (viii) 11/-12 or -10/11 , (ix) -13/5 or -4 (x) 17/(-6) or -13/4 , (xi) 7/(-9) or -5/8 , (xii) -3/(-8) or 5/9

Examine whether the following numbers are rational or irrational : (i)sqrt(5)" "(ii)sqrt(9)" "(iii)1+sqrt(2)" "(iv)2+sqrt(4) (v)sqrt(3)-sqrt(5)" "(vi)(2+sqrt(2))^(2)" "(vii)(5+sqrt(2))(5-sqrt(2))" "(viii)(sqrt(3)-sqrt(2))^(2)