Question

ATHEMATICS
(iv) 100
EXERCISE 7.1
1. Which of the following numbers are not perfect cubes?
(1) 216
(ii) 128
(m) 1000
(v) 46656
2. Find the smallest number by which each of the following numbers must be multiplied
to obtain a perfect cube.
(1) 243
(ii) 256
(ii) 72
(iv) 675
(v) 100
3. Find the smallest number by which each of the following numbers must be divided to
obtain a perfect cube.
(1) 81
(i) 128
(ii) 135
(iv) 192
(v) 704
4. Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such
cuboids will he need to form a cube?​

Answer 1

Answer:

Step-by-step explanation:

Q1.   Which of the following numbers are not perfect cubes?

           (i) 216(ii) 128(iii) 1000            (iv) 100(v) 46656Sol.     (i) We have 216 = 2 × 2 × 2 × 3 × 3 × 3                  Grouping the prime factors of 216 into triples, no factor is left over.                  ∴ 216 is a perfect cube.

                 

           (ii) We have 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2                  Grouping the prime factors of 128 into triples, we are left over with 2 as ungrouped factor.                  ∴ 128 is not a perfect cube.

                 

           (iii) We have 1000 = 2 × 2 × 2 × 5 × 5 × 5                  Grouping the prime factors of 1000 into triples, we are not left over with any factor.                  ∴ 1000 is a perfect cube.

                 

           (iv) We have 100 = 2 × 2 × 5 × 5                  Grouping the prime factors into triples, we do not get any triples. Factors 2 × 2 and 5 × 5 are not in triples.                  ∴ 100 is not a perfect cube.

                 

           (v) We have 46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3                  Grouping the prime factors of 46656 in triples we are not left over with any prime factor.                  ∴ 46656 is a perfect cube.