Question:

If \(3\sqrt{5} + \sqrt{125} = 17.88\), then what will be the value of \(\sqrt{80} + 16\sqrt{5}\)?

Show Hint

Always simplify surds to their lowest base form (like \(\sqrt{5}\)) before performing addition or substitution to avoid complex decimal calculations early on.
Updated On: May 9, 2026
  • 22.35
  • 44.7
  • 13.41
  • 21.66
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The Correct Option is B

Solution and Explanation



Step 1: Understanding the Question:

We are given the value of an expression involving surds and need to find the value of another similar expression.
We should first simplify the given expression to find the value of \(\sqrt{5}\).


Step 2: Key Formula or Approach:

Simplify the square roots by finding perfect square factors: \(\sqrt{a^2b} = a\sqrt{b}\).


Step 3: Detailed Explanation:

Given equation: \[ 3\sqrt{5} + \sqrt{125} = 17.88 \] Simplify \(\sqrt{125}\): \[ \sqrt{125} = \sqrt{25 \times 5} = 5\sqrt{5} \] Substitute this back into the equation: \[ 3\sqrt{5} + 5\sqrt{5} = 17.88 \] \[ 8\sqrt{5} = 17.88 \] Now, solve for \(\sqrt{5}\): \[ \sqrt{5} = \frac{17.88}{8} = 2.235 \] Next, we need to evaluate the target expression: \(\sqrt{80} + 16\sqrt{5}\).
Simplify \(\sqrt{80}\): \[ \sqrt{80} = \sqrt{16 \times 5} = 4\sqrt{5} \] Substitute this into the target expression: \[ 4\sqrt{5} + 16\sqrt{5} = 20\sqrt{5} \] Finally, substitute the value of \(\sqrt{5}\) we found earlier: \[ 20 \times 2.235 = 44.7 \]

Step 4: Final Answer:

The value of the expression is \(44.7\).
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