Math Problem Statement
Rasionalkan bentuk akar √8/4-√6
Solution
We are tasked with rationalizing the expression:
Step 1: Simplify
First, simplify :
Thus, the expression becomes:
Step 2: Multiply by the conjugate
To rationalize the denominator, we multiply both the numerator and the denominator by the conjugate of , which is . The conjugate helps eliminate the square root in the denominator.
So, multiply by:
This gives:
Step 3: Apply the difference of squares formula
In the denominator, use the difference of squares formula: , where and :
Thus, the expression becomes:
Step 4: Simplify the numerator
Now distribute across the terms in the numerator:
Simplify :
Thus, the numerator becomes:
Step 5: Final expression
Now, the rationalized expression is:
Simplify by dividing both terms in the numerator by 10:
Thus, the rationalized form of the expression is:
Would you like any more details or have any questions?
Related Questions:
- How do you rationalize expressions with cube roots?
- What is the general method for simplifying radicals?
- Can you explain the difference of squares formula in more detail?
- How do you simplify complex fractions involving radicals?
- What is the importance of rationalizing denominators?
Tip:
Always look for conjugates when rationalizing denominators with square roots to simplify the process.
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Math Problem Analysis
Mathematical Concepts
Algebra
Radicals
Rationalization
Conjugates
Difference of Squares
Formulas
√a × √b = √(a × b)
(a - b)(a + b) = a^2 - b^2
Theorems
Difference of Squares Theorem
Radical Simplification
Suitable Grade Level
Grades 10-12