Question

3. Find the smallest number by which the following numbers must be multiplied, so that the product is a
(V) 8640
perfect cube :
0) 2560
(ii) 7803 (iii) 8788
(iv) 1323
(v) 675
​

Answer 1

Answer:

Firstly let us find the Cube of natural numbers up to 10. 13 ... (i) 675 (ii) 1323 (iii) 2560 (iv) 7803 (v) 107811 (vi) 35721. Solution: (i) 675 ... ∴To make a perfect cube we need to multiply the product by 3 × 3 = 9. ... By which smallest number must the following numbers be divided so that the ... First find the prime factors of 8640.

Step-by-step explanation:

Answer 2

Step-by-step explanation:

) 675

First find the factors of 675

675 = 3 × 3 × 3 × 5 × 5

= 33 × 52

∴To make a perfect cube we need to multiply the product by 5.

(ii) 1323

First find the factors of 1323

1323 = 3 × 3 × 3 × 7 × 7

= 33 × 72

∴To make a perfect cube we need to multiply the product by 7.

(iii) 2560

First find the factors of 2560

2560 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5

= 23 × 23 × 23 × 5

∴To make a perfect cube we need to multiply the product by 5 × 5 = 25.

(iv) 7803

First find the factors of 7803

7803 = 3 × 3 × 3 × 17 × 17

= 33 × 172

∴To make a perfect cube we need to multiply the product by 17.

(v) 107811

First find the factors of 107811

107811 = 3 × 3 × 3 × 3 × 11 × 11 × 11

= 33 × 3 × 113

∴To make a perfect cube we need to multiply the product by 3 × 3 = 9.

(vi) 35721

First find the factors of 35721

35721 = 3 × 3 × 3 × 3 × 3 × 3 × 7 × 7

= 33 × 33 × 72