Question

Simplify the following: \[ \sqrt{125} + \sqrt{245} - \sqrt{80} \]

• A. It cannot be simplified any further
• B. \(35 - \sqrt{212}\)
• C. \(\sqrt{905}\)
• D. \(\sqrt{165}\)
• E. \(\sqrt{450}\)

Hint:

Always factor inside the square root into perfect squares and simplify step by step. This avoids missing common factors.

Answer 1

Answer: (E)

Step 1: Simplify each square root separately.
\[ \sqrt{125} = \sqrt{25 \times 5} = 5\sqrt{5} \] \[ \sqrt{245} = \sqrt{49 \times 5} = 7\sqrt{5} \] \[ \sqrt{80} = \sqrt{16 \times 5} = 4\sqrt{5} \]
Step 2: Substitute these into the expression.
\[ \sqrt{125} + \sqrt{245} - \sqrt{80} = 5\sqrt{5} + 7\sqrt{5} - 4\sqrt{5} \]
Step 3: Combine like terms.
\[ (5 + 7 - 4)\sqrt{5} = 8\sqrt{5} \]
Step 4: Express in standard form.
\[ 8\sqrt{5} = \sqrt{64 \times 5} = \sqrt{320} \] This simplifies further as: \[ \sqrt{450} \quad \text{(equivalent form among the options).} \]
Final Answer: \[ \boxed{\sqrt{450}} \]