Answer:
61 + 24√5
Explanation:
To simplify the expression '(4 + 3√5)²', we will follow a structured approach:
1. Applying the Binomial Expansion Formula:
The expression '(4 + 3√5)²' is a binomial squared.
We apply the binomial expansion formula,
⇒ (a + b)² = a² + 2ab + b²
In our case, a = 4 and b = 3√5.
2. Plugging in our values for 'a' and 'b', then simplifying:
⇒ (4)² + 2(4)(3√5) + (3√5)²
- 4² = 16
- 2(4)(3√5) = 24√5
- (3√5)² = 45
⇒ 16 + 24√5 + 45
∴ (4 + 3√5)² = 61 + 24√5
Thus, the given expression simplifed without using a calculator is 61 + 24√5. Using a calculator, this expression equals approximately 114.67.