Q13 of 76 Page 5

Prove that if a number is trebled then its cube is 27 time the cube of the given number.

Let the number is = a


Cube of number will be = a3


Now, the number is trebled = 3 × a = 3a


Cube of new number =


Hence, new cube is 27 times of original cube. Proved


More from this chapter

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11

What is the smallest number by which the following numbers must be multiplied, so that the products are perfect cubes?

(i) 675 (ii) 1323


(iii) 2560 (iv) 7803


(v) 107811 (vi) 35721

 12

By which smallest number must the following numbers be divided so that the quotient is a perfect, cube?

(i) 675 (ii) 8640


(iii) 1600 (iv) 8788


(v) 7803 (vi) 107811


(vii) 35721 (viii) 243000

 14

What happens to the cube of a number if the number is multiplied by

(i) 3?


(ii) 4?


(iii) 5?

 15

Find the value of a cube, one face of which has an area of 64m2.