6 POWER AND ROOTS EXPONENTS. Find the square roots of each of the following numbers : (i) 40 44 (iii) 78784 (iv) 8.49 (v) 0.069 (vi) 0.008 (vii).76.9 (viii) 6 (ix) 4 6 (x) (xii) (xiii) 7 49 6 Ans. (i) 40 4 4 4 0 40 840 4 68 4 4 44 4 8 6 4 (xi) 7 7 7 44 67 6 68 784 9 96 98 7 49 7 7 8 00 ICSE Math Class VII Question Bank
(iii) 78784 78784 99 69696 4848 744 87 46 78 089 6 (v) 8 (iv) 69 69 0.069 0000 0000 0000 000 00 0 849 849 8.49 00 00 00 0 6 69 4 4 4 4 4. 0 4 849 4 4 0. 00 (vi) 8 8 0.008 0000 0000 ICSE Math Class VII Question Bank
0000 000 8 7 9 00 0 6 9 0.09 00 (vii) (viii).76 76 00 76.9 00 9 9 9 76 88 44 7 6 8 9 9 6 + 6 6 08 + 6 6 6 76 9 4 6 6 6 9 (ix) 4 6 600 ICSE Math Class VII Question Bank
(x) (xi) 4 4 8 8 4 4 6 6 8 8 8 7 6 6 6 6 6 6 6 8 8 7 00 00 (xii) (xiii) 49 7 6 8 7 9 00 0 69 49 49 7 7 69 7 7 49 7 7 6 7 7 6 7 4 6 6 6 6 6 6 4. Find the cube root of : ICSE Math Class VII 4 Question Bank
(i) 4096 4666 (iii) 8000 (iv) 9 (v) 6000 (v) 79 (vi) 9 Ans. (i) Cube root of 4096 4096 Hence, 4096 6 Cube root of 4666 4666 6 6 (iii) Cube root of 8000 8000 4666 8 664 8 96 48 79 4 8 7 9 4096 048 04 6 8 64 6 8 4 ICSE Math Class VII Question Bank 8000 4000 000 000 00 0
(iv) 0 Hence, 9 4 9 07 0 7 7 (v) 6000 (6000) (vi) 6000 08000 4000 7000 00 670 7 7 Hence, cube root of 6000 ( ) 60 9 ICSE Math Class VII 6 Question Bank
9 4 7 7 7 7 7 (B) Find the cube root (i) 08 7 (iii) 0.064 (iv) 4 00 8 7 8 (v) 6 (vi) 9 6 4 (vii) [(0.8) ] () ( ) 08 7 Ans. (i) 00 0.6 (Divided by 4) 8 8 8 8 (iii) 0.064 0.064 64 000 4 4 4 4 0 0 0 0 4 0.4 0 7 4 7 + 7 8 + (iv) 4 7 8 7 8. 7 8 7 8 4 6 6 (v) 6 4 6 9 44 (vi) 9 6 4 ( ) ( ) 4 4 4 88 (vii) 6 9 (0.8) () [(0.8) () ( ) (0.8) 0.64 8 ICSE Math Class VII 7 Question Bank
0.64 40.6. Evaluate the following : (i) 6 69 6 8 (iii) 49 + 6 9 Ans. (i) 6 69 78 (iii) 6 8 49 + 6 9 4. Evaluate the following : 6 6 (i) 4 6 6 Ans. (i) 4 (iii) 7 7 + 6 7 9 9 6 6 7 7 9 79 7 + 4 9 + 7 7 8 6 7 + 7 + 4 (iii) 79 7 9 9 + 4 9 04 7 9 9 7 6 9 9 9 + 7 7 7 9 6 8 + 7. A gardener planted 484 plants in such a way that there are as many rows of the plants as their columns. How many plants are there in each row? Ans. Thus, number of plants in each row ICSE Math Class VII 8 Question Bank
484 484 4 Hence, plants are there in each row. 6. By what least number must 0808 be multiplied get a perfect square? Ans. 0808 7 7 0808 0404 0 60 867 7 89 7 7 Since one factor is not in pairs, Hence, to make it a perfect square it should be multiplied by. 7. By what the least number must 700 be divided to make it a perfect square? Ans. 700 9 9 700 600 800 90 80 9 6 9 9 Since, one factor is not in pairs Hence, the make it a perfect square it must be divided by ICSE Math Class VII 9 Question Bank
7. Ganesh planted total 66 plants in such a way that there are as many rows as 66 there are plants in each row. How many rows were there? 87 Ans. Number of total plants 66 79 Now number of rows no. of plants in each row 66 4 Number of rows 8 8 7 9 9. A teacher wanted to arrange the children of the class, 97 in number, in the form of a square. She found that there were children less. How many children did she want to put in one row? Ans. Number of children 97 Number of children which one less Total number of children required 97 + 00 As the teacher arrange the children in a square Hence, number of rows number of children in each row 00 0 0 0. 0. A gardener wanted to plant 40 plants in such a way that there are as many plants in each row as there are number of rows. He find that there are 9 extra plants. How many plants he wished to number row? Ans. Number of plants 40 Number of plants which are extra 9 Number of plants required to plants 40 9 44 As number of rows number of plants in each row 44 trees.. Find the least number by which 60 be divided to set a perfect square so obtained? Find the square root of this perfect square. ICSE Math Class VII 0 Question Bank
Ans. 60 80 40 4 60 The required number be divided to got perfect square The perfect square 60 4 4 4 6 8 7 9 Hence, the square root of 4 is 8 ICSE Math Class VII Question Bank
. A gardener planted 84 plants in the form of rows, each row containing as many plants as is the number of rows. How many plants did he plants in each row? Ans. Total number of plants to be planted 84 Number of rows Number of plants in each row Required number of plants in each row will be the square root of 84. So, 84 7 plants 7 84 9 96 648 4 6 8 7 9 Hence, the plants 7 in each row.. A group of students decided to collect as many paise from each member of the group as in the number of members. If the total collection amounts to Rs. 6., find the number of members in the group. Ans. Total amount of collection Rs 6. 6 paisa Number of members Collection from each member 6 87 6 6 7 Hence, number of member in the group are 7. ICSE Math Class VII Question Bank
4. By what least number should 88 be multiplied to get a perfect cube? What is this perfect cube. Find its cube root. Ans. 88 88 88 44 7 6 8 9 The required number be multiplied 6 The perfect cube 88 6 78 Tube root of 78 i.e. 78 Hence, cube root of 78 is.. By what least number should 09 be divided to get a perfect cube? What is this perfect cube? Find its cube root. Ans. 09 7 09 4 09 7 7 7 The required number be divided 7 49 7 7 78 864 4 6 08 4 7 9 7 4 The perfect square 09 4 The cube root of 4 7 49 7 7 ICSE Math Class VII Question Bank
Hence, 4 7 7 7 7. 6 (A) Evaluate (i) 0 6 0 9 (iii) ( 7) ( 7) ( 7) 4 0 6 0+ 6 Ans. (i) 0 6 0 9 (iii) ( 7) ( 7) ( 7) 4 ( 7) ( 7) 7 6 0 0+ 6 9 9 9 9 7 4 + 4 ( 7) ( 7) ( 7) ( 7) ( 7) ( 7) ( 7) ( 7) ( 7) 49 (B) Evaluate (i) ( 4 ) 6 (7 ) 4 (7 ) 7 (iii) (4 4 ) 0 (4 ) (4 ) Ans. (i) ( 4 ) 6 4 6 8 6 (7 ) 4 (7 ) 7 7 4 7 ( ) (( 7) 7 7 4 7 + 4 7 7 7 49 (iii) ( 4 4 ) 0 (4 ) (4 ) 4 4 0 4 4 4 0 4 6 4 4 4 0 + 6 4 4 4 4 6 (C) Evaluate (i) 8 0 6 4 4 + () 8 0 (iii) 7 + 4 6 0 6 6 Ans. (i) 8 0 6 8 6 8 6 6 64 9 4 4 + () 8 0 4 4 4 4 + 9 00 + 8 9 + 8 00 00 00 00 (iii) 7 + 4 6 0 6 6 7 + 4 4 4 6 6 + 0 84 8 84 ICSE Math Class VII 4 Question Bank
(D) Evaluate (i) + + 0 + ( + ) ( 0 ) (iii) 8 0 9 0 + + Ans. (i) + + 0 + + + + + + 60 66 + + 6 ( + ) ( 0 ) + + 9 7 + 4 8 7 7 8 (iii) 8 0 + 9 0 + + + + + + + 7. Find the value of x, when. (i) 4 9 7 x 7 0 Ans. (i) 4 9 7 x 7 0 4 x+ 9 9 7 7 x 7 0 7 + x 7 0 + x 0 x 0 8 Hence, x 8 4 x+ 9 9 4 x+ 9 9 + + 7 6 6 x+ 9 9 x + x 0 Hence x 0 (iii) ( 6 ) 4 8x ICSE Math Class VII Question Bank (iii) ( 6 ) 4 8x { (a m ) n a mn }
6 4 8x { (am) n a mn } 4 8x Ans. 8 x 4 Hence x 8. Evaluate: (i) (i) 4 a b c a b c 4 a b c a b c 4 4 a b c a b c 4 x 8 (iii) 4 (iii) 9. Evaluate (i) Ans. (i) a + b + c 4+ a b c ac b + 4 + 4 + + () 4 (4) 4 4 4 4 6 4 6 4 ICSE Math Class VII ( ) 6 (4) ( ) (4) Question Bank 4 6 6 (4) ( ) ( ) 4 ( ) ( ) 4 + 4 4+ 4 4 4 4 4 ( ) ( ) (7 ) 0 4 7 ( ) (7 ) ( ) ( ) ( ) ( ) 4 4 4 6 4 4 m m n mn mn [ ( a b ) a b ] 4 6 4 4