Math Assignment Class VIII | Cube & Cube Root CH-2

 MATH ASSIGNMENT CLASS VIII | CUBE & CUBE ROOT

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Math Assignment  Class VIII | Cube & Cube Root

Question 1
Find the smallest number by which 2250 must be multiplied so that the product is perfect cube.
Answer: 12
Question 2
Find the value of x if


Answer:  - 0.0008
Question 3
Find cube root of 175616 and use it to find the value of

Answer:  6.16
Question 4
Find the value of

Answer: 80/7
Question 5
Find the smallest number by which 8192 must be divided so that the quotient is a perfect cube.
Answer: 4
Question 6
Three numbers are in the ratio 3 : 4 : 5 and the sum of their cubes is 1728. Find numbers.

Answer:  6, 8, 10

Solution Hint:

Let numbers are 3x, 4x, 5x

ATQ (3x)³ + (4x)³ + (5x)³ = 1728

27x³ + 64x³ + 125x³ = 1728

216x³ = 1728

x³ = 1728 / 216 = 8

x = 2

Required numbers are

3x = 3 x 2 = 6

4x = 4 x 2 = 8

5x = 5 x 2 = 10

Question 7
Evaluate:

Answer: 3.24
Question 8
Write the cubes of all natural numbers between 1 and 20 and verify the following statements
a) Cubes of all odd natural numbers are odd.
b) Cubes of all even natural numbers are even.

Question 9

Write cubes of 5 natural numbers which are multiples of 3 and verify the cube of natural number, which is multiple of 3 is multiple of 27.
Solution Hint

Let first 5 multiples of 5 are: 3, 6, 9, 12, 15

3³     = 27       = 27 x 1

6³     = 216     = 27 x 8

9³     = 729     = 27 x 27

12³   = 1728   = 27 x 64

15³   = 3375   = 27 x 125

In all these cases we see that the cube of 3, 6, 9, 12, 15 is also the multiple of 27

Hence prove the required result.

Question 10
Which of the following are perfect cube
i)1728             ii) 106480.
Answer: (i) 1728 is a perfect cube

(ii) 106480 is not a perfect cube

Question 11
Which is the smallest number by which 392 must be multiplied so that the product is a perfect cube?
Answer: 7

Question 12
What is the smallest number by which 8640 must be divided so that the quotient is a perfect cube?
Answer: 5

Question 13
If one side of a cube is 13 metres, find its volume.
Answer: 13 x 13 x 13 = 2197

Question 14
Find the cube roots i) 343             ii) 1000 

                                 iii) 2744          iv) 74088      
Answer: (i) 7  (ii) 10  (iii) 14   (iii) 42

Question 15
Multiply 137592 by the smallest number so the product is a perfect cube and also find the cube root of product.
Answer

Prime factors of 137592 = 2 x 2 x 2 x 3 x 3 x 3 x 7 x 7 x 13

So if we multiply this number by 7 x 13 x 13 = 1183 then it becomes a perfect cube

137592 x 1183 = 162771336 is a perfect cube

Question 16
The volume of a cube is 343 cubic metres, find one side of cube.
Answer: 7m

Question 17
Divide the number 26244 by the smallest number so that quotient is a perfect cube. Also find the cube root of the quotient

Solution Hint:

Prime factors of 26244 = 2 x 2 x 3 x 3 x 3 x 3 x3 x 3 x3 x 3 

If we divide this number by 2 x 2 x 3 x 3 = 36, then it becomes a perfect cube

26244 ÷ 36 = 729

Question 18
The volume of cube 512 cubic metre. Find the length of the side of the cube.
Answer: 8m

Question 19
Find the cube roots of each of the following numbers 

i)   8 X 64                      ii)  - 216 X 1728        iii)  27 X (- 2744) 

iv)  -125 X -3 375         v)   - 456533              vi)  - 5832000
Answer: (i) 8   (ii) -72    (iii) - 3 x 14 = 42     (iv) 75     (v) -77       (vi) -180

Question 20
Three numbers are in the ratio 1 : 2 : 3. The sum of their cubes is 972. Find the numbers.
Answer

Solution Hint

Let numbers are:  x, 2x, 3x

(x)³ + (2x)³ + (3x)³ = 972

      x³ + 8x³ + 27x³ = 972

                       36 x³ = 972

                           x³  = 972 / 36

                           x³  = 27    ⇒  x = 3

Question 21
Difference in two perfect cubes is 189. If the cube root of smaller number is 3. Find the cube roots of the larger number.
Answer: Larger number = 6

Solution Hint

Let two numbers are a and b

a³ – b³ = 189  and  b = 3

a³ – (3)³ = 189

a³ – 27 = 189

a³ = 189 + 27

a³ = 216  ⇒ a = 6

Question 22

Evaluate:   

Answer:  8

Question 23
Evaluate:

Answer:  3/16

Question 24

If   , then find the value of x.

Ans: 0.03

Question 25

Find the smallest number by which 2880 must be divided so that the quotient is a perfect cube.

Ans. 45

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