What is the conjugate factor of [tex]$\sqrt{5}+\sqrt{2}$[/tex]?
Answer (2)
The conjugate of a + b is a − b .
The conjugate factor of 5 + 2 is 5 − 2 .
Therefore, the answer is 5 − 2 .
Explanation
Finding the Conjugate Factor The conjugate of a binomial expression of the form a + b is a − b . In our case, the expression is 5 + 2 . Therefore, the conjugate factor is 5 − 2 .
Final Answer The conjugate factor of 5 + 2 is 5 − 2 .
Examples
Conjugate factors are useful in rationalizing denominators. For example, if you have a fraction with 5 + 2 in the denominator, multiplying both the numerator and denominator by 5 − 2 will eliminate the square roots from the denominator, making the fraction easier to work with. This technique is commonly used in simplifying expressions in algebra and calculus.
The conjugate factor of 5 + 2 is 5 − 2 . This is identified by changing the sign between the two terms in the expression. Using conjugates is useful in simplifying complex mathematical expressions.
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