Solving Fractions with Roots: an Example

In summary, the conversation involves a person struggling with simplifying an expression involving fractions and square roots. They receive a hint to simplify the square root of 144 and realize their mistake. They express gratitude and apologize for overcomplicating the problem.
  • #1
james_rich
23
0
Hey having a bit of trouble with this question, not sure what to do!

QUESTION - express the fraction in the form a + b rootc / d


3 + root24 / 2 + root6

------------------------------------------
(3 + root24 / 2 + root 6) x (2 - root 6 / 2 - root 6)

Simplifying gives

(6 - 3root6 + 2root24 - root144) / -2

(6 - 3root6 + 2 x 2root6 - root144) /-2

is this right so far? the problem i am having is simplifying the root144 to a root6 inequality!
 
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  • #2
HINT: [itex]\sqrt {144} = 12[/itex]
 
  • #3
D'oh! that is so easy!

I think i tried to over complicate it! My Brain hurts! I've stared at this piece of paper for the last 10mins!

Thanx a lot, i can carry on now!

Forgive the stupidity!
 

Related to Solving Fractions with Roots: an Example

1. How do I solve fractions with roots?

To solve fractions with roots, you first need to simplify the fraction by finding the greatest common factor in the numerator and the denominator. Then, you can use the properties of exponents to simplify the roots. Finally, you can perform any necessary operations to solve the fraction.

2. Can I cancel out the roots in a fraction?

No, you cannot cancel out roots in a fraction. The properties of exponents do not allow us to cancel out roots. However, you can simplify them by using the properties of exponents.

3. How do I simplify roots in a fraction?

To simplify roots in a fraction, you can use the following properties of exponents:
- Product of Powers Property: am * an = am+n
- Quotient of Powers Property: am / an = am-n
- Power of a Power Property: (am)n = amn
- Power of a Product Property: (ab)n = an * bn
You can use these properties to simplify the roots in the numerator and denominator separately, and then simplify the resulting fraction.

4. What do I do if the fraction has a root in the denominator?

If the fraction has a root in the denominator, you can rationalize the denominator by multiplying both the numerator and denominator by the same root, or by using the conjugate of the denominator. This will eliminate the root in the denominator and make it easier to solve the fraction.

5. Can I use a calculator to solve fractions with roots?

Yes, you can use a calculator to solve fractions with roots. However, it is important to understand the concepts and steps involved in solving these fractions by hand, as it will help you better understand and use the calculator. Additionally, be sure to check your answers with the calculator to ensure accuracy.

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