Question

`3√(125) +\sqrt{(2-√(5) )^(2) }`

Answer 1

`2 + 14√(5)`

Explanation:

`\text{Simplify the surd in the first term and cancel the root and square in the second term to get} \\ \\ 15 √(5) + 2 - √(5)\\ \\ \\ \text{Add the surds together}\\\\ \\ 2 + 14√(5)`

Answer 2

`\sf 2+ 14√(5) \approx 33.30`

Explanation:

`3√(125) +\sqrt{(2-√(5) )^(2) }`

evaluating it.

Solution:

Simplify the square root of 125:

`\sf 3√(125) = 3 * √(25 * 5) = 3 * 5√(5) = 15√(5)`

Simplify the square root of
`\sf (2 - √(5))^2`:

`\sf \sqrt{(2 - √(5))^2} = (2-√(5))`

Combine the simplified terms:

`\sf 15√(5) + 2-√(5)`

combine the like terms:

`\sf 2+ 14√(5)`

Therefore, the simplified expression is
`\sf 2+ 14√(5) \approx 33.30`