Question

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

Short answer

The correct answer is 101 \(\sqrt{5}\). This means option D is the most accurate solution to the problem

Step-by-step solution

Expand the Term

Begin by expanding the term \((6+ \sqrt{5})^2 \). You can do this by applying the formula \(a^2 + 2ab + b^2\) where \(a\) is 6 and \(b\) is \(\sqrt{5}\).

Multiply each term

Next, multiply each term by \(\sqrt{5}\). Obtain \(\sqrt{5} \times 36\), \(\sqrt{5} \times 12\sqrt{5}\) and \(\sqrt{5} \times 5\). While carrying out these operations remember that \(\sqrt{5}\) squared gives \(5\).

Simplify the expression

Combine all three terms together and simplify the expression yielding the final answer.