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Cubes And Cube Roots

Question
CBSEENMA8003401
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Is 31944 a perfect cube? If not then by which smallest natural number should 31944 be divided so that the quotient is a perfect cube?

Solution

We hve 31944 = 2 x 2 x 2 x 3 x 11 x 11 x 11
Since, the prime factors of 31944 do not appear in triples as 3 is left over.

∴ 31944 is  not a perfect cube, Obviously, 31944 divided by  will be a perfect cube
i.e.          [31944] divided by 3 = [2 x 2 x 2 x 3 x 11 x 11 x 11]divided by 3
or 10648 = 2 x 2 x 2 x 11 x 11 x 11
∴ 10648 is a perfect cube.
Thus, the required  least number = 3.

Some More Questions From Cubes and Cube Roots Chapter

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. 

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

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