How to Simplify Radicals in the Denominator?

In summary, the conversation discusses simplifying the expression √8/3, and the solution is to multiply both the numerator and denominator by √3 to get 2√2/√3. It is also mentioned that the original expression could potentially be written as √(8/3), which can be simplified to √24/3. The conversation ends with determining the values of a and b in the expression √24/3 when written in the form a√b.
  • #1
kadavis2010
15
0

Homework Statement


√8/3


Homework Equations



none but there can't be any radicals in the denominator

The Attempt at a Solution


=√8/√3=2√2/√3... what do i do now.. I can't have a radical in the denominator
 
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  • #2
Hint: Multiply both the numerator and the denominator by √3.
 
  • #3
kadavis2010 said:

Homework Statement


√8/3


Homework Equations



none but there can't be any radicals in the denominator

The Attempt at a Solution


=√8/√3=2√2/√3... what do i do now.. I can't have a radical in the denominator

Why must you not have a radical in the denominator? As you wrote the original expression, you indicated [tex]\frac{\sqrt{8}}{3}[/tex]

Did you really mean to write [tex]\sqrt{\frac{8}{3}}[/tex] ? You can simplify this by multiplying by [tex]\frac{\sqrt{3}}{\sqrt{3}}[/tex], which is just a factor of 1.
 
  • #4
Yeah i meant what you said second... so would i have 24/9... with the square root of course.. but then would it be square root of 24 over 3?
 
  • #5
Yes but you can rewrite [tex] \sqrt{24} = a \sqrt{b} [/tex] What are a and b?
 

1. What does it mean to "simplify" an expression?

Simplifying an expression means to rewrite it in a more compact or concise form. This is often done by combining like terms, using the order of operations, and/or factoring out common factors.

2. Why is it important to simplify an expression?

Simplifying an expression can make it easier to understand and work with. It can also help identify patterns and relationships between different parts of the expression.

3. What are some common techniques for simplifying expressions?

Some common techniques for simplifying expressions include combining like terms, using the distributive property, factoring, and canceling out common factors.

4. Does simplifying an expression change its value?

No, simplifying an expression should not change its value. It is simply a way of rewriting the expression without changing its meaning or numerical value.

5. Can all expressions be simplified?

Not all expressions can be simplified, but most can be. It may not always be obvious how to simplify an expression, so it is important to practice and familiarize yourself with different techniques.

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