Math Problem Statement
a=Sqrt[3-Sqrt[5]]-Sqrt[3+Sqrt[5]] calcul a^2
Solution
We are given the expression:
We are asked to calculate . Let's proceed step by step:
Step 1: Square both sides of the equation.
Using the identity , we expand the square:
Step 2: Simplify the squared terms.
We can simplify the squared terms:
So, the expression becomes:
Step 3: Simplify the product inside the square root.
We now calculate , which is a difference of squares:
Thus, we have:
Step 4: Final simplification.
Thus, the value of is:
Would you like more details or have any questions?
Here are 5 questions related to this calculation:
- How does the difference of squares help simplify radical expressions?
- Can we generalize this technique for other similar expressions?
- What are the properties of square roots that allow such simplifications?
- How does this process relate to algebraic manipulation of irrational numbers?
- What would happen if the inner terms under the square roots were different?
Tip: When working with radicals, always check if you can use the difference of squares to simplify expressions efficiently.
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Math Problem Analysis
Mathematical Concepts
Algebra
Radical Expressions
Simplification
Difference of Squares
Formulas
Square of a binomial: (x - y)^2 = x^2 - 2xy + y^2
Difference of squares: (a - b)(a + b) = a^2 - b^2
Theorems
Difference of Squares Theorem
Suitable Grade Level
Grades 9-11