Page 87 - Start Up Mathematics_8 (Non CCE)

5. The cube of a natural number of the form 3n + 1, when divided by 3 leaves remainder as:
(a) 1 (b) 2 (c) 0 (d) cannot say
6. The cube of a natural number of the form 3n + 2, when divided by 3 leaves remainder as:
(a) 0 (b) 1 (c) 2 (d) 3

solve Mentally

True or False
1. 9,261 is a perfect cube.
2. There is no perfect cube that ends in 4.
3. No perfect cube can end with exactly two zeros.
3
3
4. If x divides y, then x divides y .
2
3
3
2
5. If m and n are integers such that m > n , then m > n .
3
2
6. If x ends in an even number of zeros, then x ends in an odd number of zeros.
3
2
7. If x ends in 5, then x ends in 25.
Fill in the Blanks
1. The cube of 14 = ____________.
2. The units digit of the cube of 388 is ____________.
3. If a number is multiplied by 4, its cube gets multiplied by ____________.
4. 3 2 744, =¥ _______
2
5. 3 480 = ___ ¥ 2 ¥ 3 20
3
512 8
6. 3 =
2 197 ___
,
Answer in One Word or a Line

1. Define cube of a number.
2. What is the difference between a cube and a perfect cube of a number? Explain with example.
3. What is the limitation of the method of finding cube root of a number using its units digit?
4. What will be the last digit of the cube of a number ending with 7?
5. What is radical, index and radicand? Explain with an example.

let’s evaluate
1. Find the cubes of the following numbers:
(a) 19 (b) 26 (c) 49 (d) 123
2. Find the cubes of the following by the column method:
(a) 39 (b) 46 (c) 91 (d) 87
3. Find the cube root of the following by successive subtraction:
(a) 343 (b) 216 (c) 1,000
4. Find the smallest number by which 1,458 must be divided to make it a perfect cube.
5. Find the smallest number that must be subtracted from 345 to make it a perfect cube.
6. Find the cube roots of the following:
(a) –4,913 × 512 (b) 729 × 4,096 (c) –1,331 × (–2,744)

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