How to simplify double radical when theres fractions involved?

In summary, to simplify a double radical with fractions, first simplify the fractions and combine them inside the radical. Then, find perfect square factors to simplify the radical. This process also applies when simplifying a double radical with variables and fractions. If there are different types of radicals, simplify each type separately and then combine them using the product or quotient rule. It is possible to simplify a double radical with a negative number inside, but the result may not always be a real number. Finally, there are no specific rules or formulas for simplifying double radicals with fractions, but it is helpful to remember the rules for multiplying and dividing radicals.
  • #1
needingtoknow
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Homework Statement




sqrt((2-sqrt(3))/4)

I tried to split whatever is under the radical sign into two separate parts, 1/2 and (-1/4)sqrt(3)
I realized that 1.5 times 2 is 3 and 2-1.5 = 1/2 so it seemed like it fulfilled the requirements for solving a double radical. so I put down

sqrt(3/2) - sqrt(2)

and end up with (sqrt(3) - 2)/sqrt(2) which isn't correct since the actual answer is

(sqrt(6) - sqrt(2)) / 4

What am I doing wrong?
 
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  • #2
I'm guessing that you mean this?
[tex]\sqrt{\frac{2-\sqrt{3}}{4}}[/tex]
There is a formula for simplifying double radicals. See here.
 

1. How do I simplify a double radical when there are fractions involved?

To simplify a double radical with fractions, you first need to simplify the fractions by finding the greatest common factor and dividing both the numerator and denominator by it. Then, you can combine the fractions inside the radical by adding or subtracting them. Finally, you can simplify the radical by finding perfect square factors and taking them out of the radical.

2. Can I simplify a double radical with variables and fractions?

Yes, you can simplify a double radical with variables and fractions using the same steps as with numbers. Simply simplify the fractions and combine them inside the radical, then look for any perfect square factors and take them out of the radical.

3. What do I do if there are different types of radicals in the expression?

If there are different types of radicals, you can simplify each type separately by following the same steps as with a single type of radical. Once simplified, you can then combine the different types of radicals by using the product or quotient rule for radicals.

4. Is it possible to simplify a double radical with a negative number inside?

Yes, it is possible to simplify a double radical with a negative number inside. However, the result may not always be a real number. If the radicand (number inside the radical) is negative, you can rewrite it as a positive number multiplied by -1, and then simplify as usual. However, if the radicand is a perfect square, the result will be a real number.

5. Are there any specific rules or formulas for simplifying double radicals with fractions?

There are no specific rules or formulas for simplifying double radicals with fractions. The key is to simplify the fractions and combine them inside the radical, and then simplify the radical by finding perfect square factors. It may also be helpful to remember the rules for multiplying and dividing radicals, as they can be applied when simplifying fractions inside a radical.

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