Diving Radicals
Using \/ for radical sign
7 / \/X
This book has been confusing me.
The book gives the answer 7\/X / X.
Isn't the answer 7X?
When I took algebra many many years ago they called this rationalization of the denominator. For some reason, mathematicians don't seem to like to leave fractions with a sqrt sign in the denominator. This is how you get it out.
7/(sqrt x) =
multiply by sqrt x/sqrt x to obtain
7*(sqrt x)/(sqrt x)*(sqrt x) =
7*(sqrt x)/x.
Simplify. Write each answer in scientific notation.
1) (5.86 × 100
)(7.99 × 100
)
Let's break down the problem to understand it better. In the given expression, we have 7 divided by the square root of X (written as 7 / √X).
To simplify this expression, our goal is to eliminate the radical in the denominator (the square root of X). To do that, we can use a property of radicals called "rationalizing the denominator."
Rationalizing the denominator involves multiplying the numerator and denominator of the expression by the conjugate of the denominator.
For a radical expression like √X, the conjugate is √X itself. So, we multiply the numerator and denominator of 7 / √X by √X:
(7 / √X) * (√X / √X)
Now, let's simplify this expression:
(7 * √X) / (√X * √X)
In the denominator, √X multiplied by √X is equal to X:
(7 * √X) / X
So, the simplified expression is 7√X divided by X, written as 7√X / X.
Therefore, the book is correct in stating that the answer is 7√X / X. It is not equal to 7X.