With great difficulty. What exactly are you trying to ask?
Real numbers are closed under addition and subtraction. To get a number outside the real number system you would have to use square root.
The only whole number square between 29 and 42 is 36 .
Prime numbers can't have whole number square roots, of course, but the largest prime number under 400 is 397.
There are 5 square numbers under 30: 1, 4, 9, 16, and 25.
No. For example, the square root of two plus (minus the square root of two) = 0, which is not an irrational number.
Real numbers are closed under addition and subtraction. To get a number outside the real number system you would have to use square root.
The only whole number square between 29 and 42 is 36 .
That depends what set of numbers you are thinking of; but in the case of the sets commonly used - integers, rational numbers, real numbers, complex numbers - such sets are closed under multiplication, meaning that you can multiply any number in the set by any number in the set, so there is nothing to stop you multiplying such a number by itself.
Prime numbers can't have whole number square roots, of course, but the largest prime number under 400 is 397.
There are 5 square numbers under 30: 1, 4, 9, 16, and 25.
No. Negative numbers are real but their square roots are not.
No. For example, the square root of two plus (minus the square root of two) = 0, which is not an irrational number.
The nearest number whose square ≤ 10000 is 100. Then the greatest odd number less that 100 is 99 so there are 50 odd numbers in the range 1- 99 inclusive whose squares are less than 10000.
A perfect square is a square of an integer.The set of integers is closed under multiplication. That means that the product of any two integer is an integer. Therefore the square of an integer is an integer.Integers are rational numbers so the square [which is an integer] is a rational number.
If the number under the radical sign has a factor which is a square number greater than 1, then the square root of that number can be taken outside the radical.For example,sqrt(75) = sqrt(25*3) = sqrt(25)*sqrt(3) = 5*sqrt(3).
It would be an imaginary number (one that cannot exist). For example the square root of a negative number.
Oh, what a lovely question! You see, for the square root of 'n' to be a rational number, 'n' must be a perfect square. When 'n' is a perfect square, the square root of 'n' will be a whole number, which is a rational number. Just like painting happy little trees, mathematics can be a beautiful and harmonious world when we understand its patterns and shapes.