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प्रश्न
Prove that if a number is trebled then its cube is 27 times the cube of the given number.
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उत्तर
Let us consider a number n. Then its cube would be \[n^3\] .
If the number n is trebled, i.e., 3n, we get:
\[\left( 3n \right)^3 = 3^3 \times n^3 = 27 n^3\]
It is evident that the cube of 3n is 27 times of the cube of n.
Hence, the statement is proved.
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संबंधित प्रश्न
Find the smallest number by which the following number must be multiplied to obtain a perfect cube.
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Show that: \[\sqrt[3]{27} \times \sqrt[3]{64} = \sqrt[3]{27 \times 64}\]
Making use of the cube root table, find the cube root
700
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Find the cube-root of 8000.
Find the cube-root of `343/512`
Find the cube-root of 64 x 729
Evaluate:
`root(3)(27) + root(3)(0.008) + root(3)(0.064)`
