Final answer:
The given radical expression √(2+3)(5-7) is simplified by using the distributive property to multiply each term in the first radical by each term in the second, resulting in √10 - √14 + √15 - √21.
Step-by-step explanation:
The student's question involves simplifying a radical expression which is a fundamental concept in algebra, typically covered in high school mathematics. The expression in question is √(2+3)(5-7). To simplify this expression, one must apply the distributive property, also known as FOIL (First, Outer, Inner, Last) when dealing with binomials.
To demonstrate, let's perform the multiplication step-by-step:
Multiply the First terms: √2 * √5 = √(2*5) = √10.Multiply the Outer terms: √2 * (-√7) = -√(2*7) = -√14.Multiply the Inner terms: √3 * √5 = √(3*5) = √15.Multiply the Last terms: √3 * (-√7) = -√(3*7) = -√21.
Combining these products gives us the simplified form of the expression:
√10 - √14 + √15 - √21
No further simplification can be made unless we have additional constraints or we consider approximate decimal values. It is essential to eliminate terms wherever possible. However, in this case, there are no like terms to combine. Finally, always check the answer to ensure it is reasonable, which means re-evaluating the steps you have taken and verifying that all mathematical principles have been correctly applied.