Page 86 - Start Up Mathematics_8 (Non CCE)

4. Find the cube roots of the following rational numbers:
729 -3 375, 24 389, 9 261, -21 952,
(a) (b) (c) (d) (e)
2 197, 4 913, 19 683, - 1 000, 6 859,

5. Find the smallest number by which –6,125 should be multiplied to make it a perfect cube.
6. Find the smallest number by which –250 should be divided to make it a perfect cube.
3
7. The volume of a cuboidal box is 35.937 m . Find the side of the box.
2 197, 3
8. The volume of a cube is cm . Find its side.
729
9. Three numbers are in the ratio 3 : 4 : 5. The sum of their cubes is 0.001728. Find the numbers.
10. Three numbers are in the ratio 2 : 3 : 5. The sum of their cubes is 54,880. Find the numbers.
11. Two numbers are in the ratio 2 : 3. The difference of their cubes is 9,728. Find the numbers.

AT a Glance

3
1. The cube of a number is the number raised to the power 3, i.e., if x is a number, then x is its cube where
3
x = x × x × x.
3
2. A natural number n is a perfect cube, if n = m for some natural number m.
3. The cube of an even natural number is even.
4. The cube of an odd natural number is odd.
5. The sum of the cubes of n-natural numbers is equal to the square of their sum
3
3
2
3
3
i.e., 1 + 2 + 3 + ... + n = (1 + 2 + 3 + ... + n) .
3
6. A number m is the cube root of a natural number n, if n = m , i.e., n is the number whose cube is n.
3
3
7. For any positive integer n, -= -n 3 n.
8. For any two integers x and y, xy = 3 x ¥ 3 y.
3
p p 3 p
9. For any rational number q , q π 0, 3 q = 3 q .

Review Exercises

Multiple ChoiCe Questions

1. Cube of an odd natural number is:

(a) a prime number (b) an even natural number
(c) an odd natural number (d) none of these
2. Cube root of –729 is:
(a) 9 (b) –9 (c) 81 (d) –3
3. Cube root of the product of a positive and a negative number is:
(a) a prime number (b) a positive number
(c) a negative number (d) may be positive or negative

4. The value of 3 -3 3 is:
3
3
(a) –3 (b) 3 (c) –3 (d) 3
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