Table of Contents
- 1 What is the smallest positive integer n such that 2n is a perfect square and 3n is a perfect cube?
- 2 What is the smallest natural number that is both a perfect square and a perfect cube?
- 3 What is the smallest integer greater than 1 such that 1/2 of a perfect square and 1/5 of it is a perfect fifth power?
- 4 What is the only integer between 2 and 100 that is both a perfect square and a perfect cube?
- 5 How do you find a perfect square of a number?
- 6 IS 111 a perfect square?
What is the smallest positive integer n such that 2n is a perfect square and 3n is a perfect cube?
If a number is a perfect square, then all of the exponents in this representation have to be divisible by 2. So 9 = 3^2 is a perfect square, but 27 = 3^3 is not. If it is a perfect cube, all the exponents have to be divisible by 3. so 8 = 2^3 is a perfect cube, but 16 = 2^4 is not.
What is the smallest natural number that is both a perfect square and a perfect cube?
The answer is the only number in both lists: 64.
How do you determine if a number is a perfect square or perfect cube?
If a variable with an exponent has an exponent which is divisible by 3 then it is a perfect cube. To get the cube root, we simply divide the exponent by 3. For example x9 is a perfect cube, its cube root is x3 .
IS 144 a perfect cube or square?
144 is equal to 12 squared, and so is a perfect square. 5 cubed is 125 and 6 cubed is 216, so the cube root of 144 is between 5 and 6 and so 144 is not a perfect cube. So, it is a perfect square, but not a perfect cube.
What is the smallest integer greater than 1 such that 1/2 of a perfect square and 1/5 of it is a perfect fifth power?
The answer is 500000. Done.
What is the only integer between 2 and 100 that is both a perfect square and a perfect cube?
the numbers i know are 64 and 729 which is both a sqr and a cube.
How do you find numbers that are both perfect squares and cubes?
A perfect cube is obtained when a power which is a multiple of 3 is present on a number. Hence a number which is both a perfect square and a perfect cube must be obtained by the presence of power which a multiple of 2*3=6. Therefore such numbers are, 0^6 = 0, 1^6 = 1, 2^6 = 64, 3^6 = 729 and so on.
Is the number 2 a perfect square?
For instance, the product of a number 2 by itself is 4. In this case, 4 is termed as a perfect square. A square of a number is denoted as n × n. Similarly, the exponential notation of the square of a number is n 2, usually pronounced as “n” squared….Example 1.
| Integer | Perfect square |
|---|---|
| 2 x 2 | 4 |
| 3 x 3 | 9 |
| 4 x 4 | 16 |
| 5 x 5 | 25 |
How do you find a perfect square of a number?
You can also tell if a number is a perfect square by finding its square roots. Finding the square root is the inverse (opposite) of squaring a number. If you find the square root of a number and it’s a whole integer, that tells you that the number is a perfect square. For instance, the square root of 25 is 5.
IS 111 a perfect square?
Is the number 111 a Perfect Square? The prime factorization of 111 = 31 × 371. Therefore, 111 is not a perfect square.
IS 222 a perfect square?
Is the number 222 a Perfect Square? The prime factorization of 222 = 21 × 31 × 371. Therefore, 222 is not a perfect square.
Is 81 a square number?
Informally: When you multiply an integer (a “whole” number, positive, negative or zero) times itself, the resulting product is called a square number, or a perfect square or simply “a square.” So, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on, are all square numbers.