Question

How do I rationalize the denominator?

1/√8

a) Multiply by (√8)
b) Divide by (√8)
c) Multiply by (√2)
d) Divide by (√2)

Answer 1

Rationalizing the denominator of 1/√8 involves multiplying both the numerator and denominator by √8, simplifying, and then reducing the fraction to get the final answer of √2/4.

Step-by-step explanation:

To rationalize the denominator of the fraction 1/√8, you need to eliminate the radical from the denominator. The process involves multiplying both the numerator and the denominator by a value that will create a perfect square under the radical in the denominator, which in this case is √8. Here's how you do it:

1. Multiply both the numerator and denominator by √8 to get (1 * √8)/(√8 * √8).
2. Simplify to √8/8.
3. Now recognize that √8 can be simplified further to 2√2 because √8 = √(4*2) = √4 * √2 = 2√2.
4. This gives you the simplified answer of 2√2/8.
5. Finally, reduce the fraction by dividing both the numerator and the denominator by 2 to get √2/4.