Why is raising a number to the power of 1/2 the same as finding the square root of the number?
Can someone please help. Please provide examples. I would appreciate it if you guys can help as soon as possible.
Patience, child. I've deleted 3 of these duplicate posts in the last few minutes. Do not post this question again for at least 3 hours.
Sorry, I didn't know that you delete duplicate posts. I have only just started using this site a couple days ago.
We know that
(√x)^2 = x , by the very definition of √x
suppose we take x(1/2) and square it
(x^(1/2)^2
by the exponents rules this would be
x( (1/2)(2) )
= x
so (√x)^2 = (x^(1/2) )^2
then √x = x^(1/2)
so x^(1/2) behaves the same way as √x
by the same argument we can show that
x^(1/3) is the same as ∛x
x^(1/4) is the same as ∜x
etc
Thank you. I appreciate it.
Raising a number to the power of 1/2 is the same as taking the square root of that number. This is because raising a number to the power of 1/2 means finding the value that, when multiplied by itself, gives you the original number. The square root of a number is basically asking "what number, when multiplied by itself, gives you the original number?"
Let's take an example to understand it better. Suppose we have the number 25.
If we raise 25 to the power of 1/2:
25^(1/2) = √25
The answer to this expression is 5, which is also the square root of 25. This is because 5 multiplied by itself equals 25.
Let's take another example with a different number. Suppose we have the number 16.
If we raise 16 to the power of 1/2:
16^(1/2) = √16
The answer to this expression is 4, which is also the square root of 16. Again, this is because 4 multiplied by itself equals 16.
In conclusion, raising a number to the power of 1/2 is equivalent to finding the square root of that number.