Complete this item.
The conjugate of $12-\sqrt{5}$ is

The conjugate of the expression 12 − 5 ​ is 12 + 5 ​ . This is found by identifying the components of the expression and changing the sign between them. Therefore, the final answer is 12 + 5 ​ ​ .
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Answered by Anonymous | 2025-07-04

The conjugate of a number in the form a − b is a + b .
Identify a = 12 and b = 5 ​ in the expression 12 − 5 ​ .
Determine the conjugate by changing the sign between the terms.
The conjugate of 12 − 5 ​ is 12 + 5 ​ ​ .

Explanation

Identifying the Conjugate Form The conjugate of a number in the form a − b is a + b . In this case, we have 12 − 5 ​ , so a = 12 and b = 5 ​ .

Determining the Conjugate Therefore, the conjugate of 12 − 5 ​ is 12 + 5 ​ .


Examples
Conjugates are useful in simplifying expressions, especially when dealing with complex numbers or radicals in the denominator of a fraction. For example, if you have a fraction like 12 − 5 ​ 1 ​ , you can multiply both the numerator and denominator by the conjugate 12 + 5 ​ to rationalize the denominator, resulting in ( 12 − 5 ​ ) ( 12 + 5 ​ ) 12 + 5 ​ ​ = 144 − 5 12 + 5 ​ ​ = 139 12 + 5 ​ ​ . This technique is commonly used in algebra and calculus to simplify expressions and solve equations.

Answered by GinnyAnswer | 2025-07-04