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Cubes And Cube Roots

Question
CBSEENMA8003450
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Is 216 a perfect cube? What is the number whose cube is 216?

Solution

We have 216

i.e. Resolving 216 into prime factors we have: 216 = 2 x 2 x 2 x 3x 3 x 3

i.e. 216 can be resolved in to such prime factor which can be grouped into triple of equal of factor and no factor is left over.

∴ 216 is a perfect cube

Thus, the required number is 6, whose cube is 216.

 

Some More Questions From Cubes and Cube Roots Chapter

Is 500 a perfect cube?

Is 1372 a perfect cube? If not, find the smallest natural number by which 1372 must be multipled so that the product is a perfect cube.

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. 

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