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Cubes And Cube Roots

Question
CBSEENMA8003483
Wired Faculty App

Show that 0.001728 is the cube of a rational number. Find that rational number whose cube is 0.0017288.

Solution

We have
space space space space 0.001728 space equals space 1728 over 1000000
Now,  
 

∴    space space space space 1728 over 1000000 space equals space fraction numerator 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 3 cross times 3 cross times 3 over denominator 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 5 cross times 5 cross times 5 cross times 5 cross times 5 cross times 5 end fraction
                        space space space space equals space fraction numerator 3 cross times 3 cross times 3 over denominator 5 cross times 5 cross times 5 cross times 5 cross times 5 cross times 5 end fraction
                        space space equals fraction numerator 3 cubed over denominator 5 cubed cross times 5 cubed end fraction
                   space space space space space space space equals open parentheses fraction numerator 3 over denominator 5 cross times 5 end fraction close parentheses cubed

∴   space space space space space space space space space space space space space space cube root of 1728 over 1000000 end root equals space open parentheses fraction numerator 3 over denominator 5 cross times 5 end fraction close parentheses cubed
space space space space space space space rightwards double arrow space space space space space space space cube root of 1728 over 1000000 end root equals fraction numerator 3 over denominator 5 cross times 5 end fraction
     rightwards double arrow space space space space space space cube root of 0.001728 end root space equals space 3 over 25
Thus, 0.001728 is the cube of space 3 over 25.

 

 

Some More Questions From Cubes and Cube Roots Chapter

Find the one’s digit of the cube of each of the following numbers.

(i) 3331 (ii) 8888 (iii) 149 (iv) 1005

(v) 1024 (vi) 77 (vii) 5022 (viii) 53

Consider the following pattern:



Express the following numbers as the sum of odd numbers using the above pattern?

(a) 63 (b) 83 (c) 73

Which of the following are perfect cubes?

1. 400 2. 3375 3. 8000 4. 15625

5. 9000 6. 6859 7. 2025 8. 10648

Check which of the following are perfect cubes.

(i) 2700 (ii) 16000 (iii) 64000 (iv) 900

(v) 125000 (vi) 36000 (vii) 21600 (viii) 10000

(ix) 27000000 (x) 1000

What pattern do you observe in these perfect cubes?

Which of the following numbers are not perfect cubes? (i) 216 (ii) 128 (iii) 1000 (iv) 100 (v) 46656

Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. (i) 243 (ii) 256 (iii) 72 (iv) 675 (v) 100

Show that —1728 is a perfect cube. Also, find the number whose cube is – 1728. 

Is 216 a perfect cube? What is the number whose cube is 216?

Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube?

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