2-solution.jpeg "(√3+√7)2 Solution")
Solving (√3+√7)²
In this article, we will solve the problem of evaluating the expression (√3+√7)².
The Problem
Given the expression (√3+√7)², we need to evaluate it and simplify the result.
Step-by-Step Solution
To evaluate the expression, we can start by using the formula for the square of a sum:
(a+b)² = a² + 2ab + b²
In this case, a = √3 and b = √7. Plugging these values into the formula, we get:
(√3+√7)² = (√3)² + 2(√3)(√7) + (√7)²
Simplifying the Expression
Now, let's simplify each term:
- (√3)² = 3
- 2(√3)(√7) = 2√21
- (√7)² = 7
So, the expression becomes:
(√3+√7)² = 3 + 2√21 + 7
Combining Like Terms
Combining like terms, we get:
(√3+√7)² = 10 + 2√21
And that's the final result!
Conclusion
In this article, we have evaluated the expression (√3+√7)² and simplified it to 10 + 2√21. This problem illustrates the application of the formula for the square of a sum, and how to simplify expressions involving radicals.
