Dividing Radicals
Using \/ for radical sign
\/3X / \/3
Answer in the book is 1/3 \/9X.
I thought you divide the top and bottom by 3. Then multiply. I did not arrive at the answer.
The answer in the book is silly. What is the sqrt (9)?
To divide radicals, we can use the concept of rationalizing the denominator. This involves multiplying the numerator and denominator by the conjugate of the denominator, which is the expression obtained by changing the sign of the radical.
In this case, we want to divide \/3X by \/3. To do this, we can multiply both the numerator and the denominator by the conjugate of \/3, which is also \/3.
Here are the steps:
Step 1: Multiply the numerator and the denominator by the conjugate of the denominator:
(\/3X * \/3) / (\/3 * \/3)
Step 2: Simplify the expression by applying the product of radicals rule:
(\/(3X * 3)) / (\/(3 * 3))
Step 3: Simplify further:
(\/(9X)) / (\/(9))
Step 4: Apply the rule of dividing radicals with the same index:
(1 / 3) * (\/9X)
Therefore, the final answer is 1/3 * \/9X, which matches the answer in the book.