How to simplify double radical when theres fractions involved?

Click For Summary
SUMMARY

The discussion focuses on simplifying the double radical expression sqrt((2-sqrt(3))/4). The user initially attempted to separate the components under the radical but arrived at an incorrect result of (sqrt(3) - 2)/sqrt(2). The correct simplification is (sqrt(6) - sqrt(2)) / 4, which adheres to the established formula for simplifying double radicals. The conversation highlights the importance of correctly applying algebraic techniques to achieve accurate results.

PREREQUISITES
  • Understanding of radical expressions and their properties
  • Familiarity with algebraic manipulation techniques
  • Knowledge of simplifying fractions involving radicals
  • Experience with double radical simplification methods
NEXT STEPS
  • Study the formula for simplifying double radicals in detail
  • Practice additional examples of radical simplification
  • Learn about the properties of square roots and their applications
  • Explore techniques for handling complex fractions in algebra
USEFUL FOR

Students studying algebra, mathematics educators, and anyone looking to enhance their skills in simplifying radical expressions.

needingtoknow
Messages
160
Reaction score
0

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?
 
Physics news on Phys.org
I'm guessing that you mean this?
\sqrt{\frac{2-\sqrt{3}}{4}}
There is a formula for simplifying double radicals. See here.
 

Similar threads

Replies
13
Views
3K
Replies
4
Views
4K
  • · Replies 41 ·
2
Replies
41
Views
6K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
9
Views
2K
  • · Replies 39 ·
2
Replies
39
Views
4K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K