Given 3√5 + √125 = 17.88, find the value of √80 + 6√5.

Problem restatement
Use the given radical equation to evaluate √80 + 6√5.

Given data

• 3√5 + √125 = 17.88

Concept/Approach
Simplify √125 and √80 in terms of √5; then substitute the derived value of √5.

Step-by-step calculation
√125 = √(25 × 5) = 5√53√5 + 5√5 = 8√5 = 17.88 ⇒ √5 = 17.88 / 8 = 2.235√80 = √(16 × 5) = 4√5√80 + 6√5 = (4 + 6)√5 = 10√5 = 10 × 2.235 = 22.35

Verification/Alternative
Directly, √80 + 6√5 = 4√5 + 6√5 = 10√5, which follows from the given equation.

Common pitfalls
Not simplifying radicals to a common base (√5), or approximating √5 prematurely.

Final Answer
22.35