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Is 72 a perfect square?
NO. 72 = 2 x 36 = 2 x 62 and 72 = 8 x 9 = 8 x 32 Some of the factors of 72 can be represented as perfect squares but not all the factors, hence 72 itself is NOT a perfect square number.
Is the square root of 72 a rational or irrational number?
The square root of 72 is an irrational number. Since 72 is not a perfect square, the decimal is endless. (just like the value of pi)
What is the highest common factor of 40 and 72?
The highest common factor (HCF) of 40 and 72 is the largest number that divides both 40 and 72 without leaving a remainder. To find the HCF, we need to identify the common factors of 40 and 72, which are 1, 2, 4, and 8. The highest common factor of 40 and 72 is 8.
What is the greatest common factor of 16 40 and 72?
The greatest common factor is the highest number that divides exactly into two or more numbers. 16: 1, 2, 4, 8, 16 40: 1, 2, 4, 5, 8, 10, 20, 40 72: 1, 2, 3, 4, 6,8, 9, 12, 18, 24, 36, 72 The greatest common factor of 16, 40 and 72 is 8.
What is the smallest positive integer n such that 2n is a perfect square and 3n is a perfect cube?
n=72 satisfies the relation. 2*72 = 12**2, and 3*72 = 6**3. The only question is whether or not that is the smallest integer that will do so. All perfect squares of which 2n is a factor are of form (2x)**2 = 4x**2, with n= 2x**2. Similarly all perfect cubes of which 3n is a factor are of form (3y)**3 = 27y**3 with n = 9y**3. So, we need integers x and y such that 2x**2 = 9y**3. If the integers x and y are the smallest that satisfy the equation, then we have the smallest n. It doesn't work for y = 1, or any other odd number. If y = 2, n = 72. There is a number x =6 which satisfies the relation. Since y is smallest possible, then n=72 is the smallest positive integer that satisfies the relation.
