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प्रश्न
Find the smallest number by which 200 should be multiplied to make it a perfect cube
उत्तर
| 2 | 200 |
| 2 | 100 |
| 2 | 50 |
| 5 | 25 |
| 5 | 5 |
| 1 |
We find 200 = `bar(2 xx 2 xx 2) xx 5 xx 5`
Grouping the prime factors of 200 as triplets, we are left with 5 × 5
We need one more 5 to make it a perfect cube.
So to make 200 a perfect cube multiply both sides by 5.
200 × 5 = `(bar(2 xx 2 xx 2) xx 5 xx 5) xx 5`
1000 = 2 × 2 × 2 × 5 × 5 × 5 × 5 × 5
Now 1000 is a perfect cube.
∴ The required number is 5.
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संबंधित प्रश्न
Write the cubes of 5 natural numbers which are of the form 3n + 1 (e.g. 4, 7, 10, ...) and verify the following:
'The cube of a natural number of the form 3n + 1 is a natural number of the same form i.e. when divided by 3 it leaves the remainder 1'.
What happens to the cube of a number if the number is multiplied by 5?
Write the units digit of the cube of each of the following numbers:
31, 109, 388, 833, 4276, 5922, 77774, 44447, 125125125
Which of the following number is not perfect cubes?
64
Which of the following number is not perfect cubes?
216
Show that:
\[\frac{\sqrt[3]{729}}{\sqrt[3]{1000}} = \sqrt[3]{\frac{729}{1000}}\]
Find the cube-root of 4096.
Find the cube-root of -216
Find the cube-root of 2.744
Cube roots of 8 are +2 and –2.
