Simplify √(5)(6+√(5))^2 (A) 41+2 √(5) (B) 53 √(5) (C) 41 √(5)+60 (D 101 √(5

step 1 Okay, so we want to simplify our following expression here. So I'm going to expand this power of

Simplify √(5)(6+√(5))^2 (A) 41+2 √(5) (B) 53...

$$\text { Simplify } \sqrt{5}(6+\sqrt{5})^{2}$$
$$\begin{array}{llllll}
\text { (A) } 41+2 \sqrt{5} & \text { (B) } 53 \sqrt{5} & \text { (C) } 41 \sqrt{5}+60 & \text { (D } 101 \sqrt{5}
\end{array}$$

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Key Concepts

Binomial Expansion

Binomial expansion is a technique used to expand expressions raised to a power, commonly using the formula (a + b)^2 = a^2 + 2ab + b^2. This method is essential for breaking down complex expressions into simpler components, allowing each term to be individually manipulated or simplified.

Multiplication of Radical Terms

Multiplication of radical terms involves applying the property ?a * ?b = ?(a*b). This property is fundamental in algebra for combining or simplifying expressions with square roots, and it often enables the conversion of radical products into integer values when perfect squares are involved.

Distributive Property

The distributive property asserts that multiplying a sum by a factor is equivalent to multiplying each addend by the factor and then summing the results. This property is crucial for expanding expressions efficiently and is widely used when dealing with both numeric and radical terms.

Simplification of Radical Expressions

Simplifying radical expressions involves reducing square roots and other roots to their simplest form by identifying and extracting perfect square factors. This process is key in ensuring that expressions with radicals are expressed in their most reduced and understandable form, facilitating easier computation and comparison.

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