Math Problem Statement
The rationalising factor of 4 root 5 - 1
Solution
To rationalize the expression , we can multiply the numerator and denominator by the conjugate of the expression. The conjugate of is .
So, we multiply:
The denominator simplifies using the difference of squares:
Thus, the rationalized form is:
Would you like further details on any step, or do you have any questions? Here are some related questions you might find interesting:
- What is the significance of rationalizing denominators in mathematics?
- Can you provide another example of rationalizing a different expression?
- How does rationalizing affect the value of an expression?
- What is the general form of a conjugate for a binomial expression?
- Why do we prefer rationalizing expressions in certain mathematical contexts?
Tip: Always use the conjugate to simplify expressions involving square roots or other irrational numbers.
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Math Problem Analysis
Mathematical Concepts
Algebra
Rationalizing Expressions
Conjugates
Formulas
Rationalizing formula: \( \frac{a}{b} \cdot \frac{c}{c} = \frac{ac}{bc} \)
Difference of squares: \( a^2 - b^2 = (a-b)(a+b) \)
Theorems
Conjugate theorem
Suitable Grade Level
Grades 9-12