how many perfect cubes lie between 2^7+1 and 2^18+1
52 , 50 ,59, 54
Answers
Answer:
The final answer is 58.
Step-by-step explanation:
We need to find the total number of cubes that lie between 2 ^ 7 + 1 and 2 ^ 18 + 1.
A perfect cube can be defined as a number obtained by multiplying a number with itself 3 times. That is consider x to be a random number then the cube of the number is y where,
x * x * x = y
Y is a perfect cube as it is a number that can be obtained by multiplying one number thrice with itself.
2 ^ 7 + 1 = 129
2 ^ 18 + 1 = 2,62,145
The first cube more than 129 is 216 = 6.
The last cube less than 2,62,145 is 2,62,144 = 64.
64 - 6 = 58
The number of perfect cubes is 58.
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Answer:
The answer is 58 in the end.
Detailed explanation:
Finding the total number of cubes between 2 + 7 + 1 and 2 + 18 + 1 is necessary.
A number that is produced by multiplying a number by itself three times is known as a perfect cube. In other words, if x is taken as a random number, then y is the number's cube.
x * x * x = y
Y is a perfect cube since it can be calculated by multiplying a single number three times with itself.
2 ^ 7 + 1 = 129
2 ^ 18 + 1 = 2,62,145
The first cube over 129 is 216, which equals 6.
2,62,144 = 64 is the last cube below 2,62,145.
64 - 6 = 58
There are 58 perfect cubes in existence.
A perfect cube of a number is a number that is equal to the number, multiplied by itself, three times. If x is a perfect cube of y, then x = y3. Therefore, if we take the cube root of a perfect cube, we get a natural number and not a fraction. Hence, 3√x = y. For example, 8 is a perfect cube because 3√8 = 2
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