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प्रश्न
Which of the following is perfect cube?
3087
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उत्तर
On factorising 3087 into prime factors, we get:
\[3087 = 3 \times 3 \times 7 \times 7 \times 7\]
Group the factors in triples of equal factors as:
\[3087 = 3 \times 3 \times \left\{ 7 \times 7 \times 7 \right\}\]
It is evident that the prime factors of 3087 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 243 is a not perfect cube.
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संबंधित प्रश्न
Write the cubes of 5 natural numbers of the form 3n + 2 (i.e. 5, 8, 11, ...) and verify the following:
'The cube of a natural number of the form 3n + 2 is a natural number of the same form i.e. when it is dividend by 3 the remainder is 2'.
Which of the following is perfect cube?
243
Which of the following number is not perfect cubes?
216
Find the cube root of the following natural number 134217728 .
Find the units digit of the cube root of the following number 175616 .
Making use of the cube root table, find the cube root
780 .
Find the cube-root of `125/216`
Find the cube-root of -2197.
Find the cube-root of -0.512
Evaluate:
`root(3)(27) + root(3)(0.008) + root(3)(0.064)`
