Explain why (-9)1/2 is not a real number but -9 1/2 is a real number.
(-9)1/2 = -4.5 which is a real number.
Unless you're talking about square roots?
No I'm not talking about square roots.
If you are talking about powers,
9^(1/2) = 3
x^(1/2) = √x so you are talking about square roots.
(-9)^(1/2) is not real, because negative numbers do not have real square roots.
That is because if x = √(-9) then x^2 = -9. But all numbers are positive when squared.
Well, (-9)^(1/2) is not a real number because it involves taking the square root of a negative number. Just like trying to find the positive square root of -9 would leave you scratching your head, this expression leaves mathematicians scratching their heads too. It's like trying to find a four-leaf clover in a desert – you're just not going to have any luck!
On the other hand, -9 1/2 is a real number. It's a simple addition problem! Just take the number -9 and add 1/2 to it. It may not be the most exciting real number in the world, but at least it exists and doesn't leave mathematicians feeling perplexed. It's like finding a plain old rock on the ground – not the most exciting thing, but at least it's there for you to hold onto!
To understand why (-9)^(1/2) is not a real number while -9 1/2 is a real number, we need to examine the concept of square roots.
In mathematics, a square root is a value that, when multiplied by itself, gives the original number. For example, the square root of 4 is 2 because 2 * 2 = 4.
Now, let's look at (-9)^(1/2):
To calculate this, we need to consider the property of even roots. For even roots (such as square roots), the result is undefined for negative numbers. This means that (-9)^(1/2) does not produce a real number.
However, if we write -9 1/2, we are expressing a mixed number. In this case, the whole number part is -9, and the fractional part is 1/2.
A mixed number can be represented as a sum of a whole number and a fraction. In this case, -9 1/2 can be written as -9 + 1/2.
The whole number -9 is a real number, and the fractional part 1/2 is also a real number. When we add these two real numbers together, the result is a real number. Therefore, -9 1/2 is a real number.
In summary, (-9)^(1/2) is not a real number because the square root of a negative number is undefined for even roots. On the other hand, -9 1/2 is a real number because it represents a sum of a whole number and a fraction, both of which are real numbers.