Question:
Simplify the following: \(40 - \sqrt{420} - \sqrt{20} - \sqrt{160}\).
Simplify the following: \(40 - \sqrt{420} - \sqrt{20} - \sqrt{160}\).
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Simplify each square root individually. If radicals do not match, the expression cannot be reduced further.
Updated On: Oct 3, 2025
- \(5 - \sqrt{(5+22-\sqrt{)}}\)
- The expression cannot be simplified any further
- \(\sqrt{810}\)
- \(10 - \sqrt{(6+2-\sqrt{)}}\)
- \(\sqrt{420}\)
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The Correct Option is B
Solution and Explanation
Step 1: Break down terms.
The terms inside radicals are not perfect squares: \[ \sqrt{420}, \ \sqrt{20}, \ \sqrt{160} \] Step 2: Simplify if possible.
- \(\sqrt{20} = 2\sqrt{5}\)
- \(\sqrt{160} = 4\sqrt{10}\)
- \(\sqrt{420} = 2\sqrt{105}\)
Step 3: Combine.
Final = \(40 - 2\sqrt{105} - 2\sqrt{5} - 4\sqrt{10}\). Since no further simplification is possible, answer remains as is. Final Answer: \[ \boxed{\text{The expression cannot be simplified further.}} \]
The terms inside radicals are not perfect squares: \[ \sqrt{420}, \ \sqrt{20}, \ \sqrt{160} \] Step 2: Simplify if possible.
- \(\sqrt{20} = 2\sqrt{5}\)
- \(\sqrt{160} = 4\sqrt{10}\)
- \(\sqrt{420} = 2\sqrt{105}\)
Step 3: Combine.
Final = \(40 - 2\sqrt{105} - 2\sqrt{5} - 4\sqrt{10}\). Since no further simplification is possible, answer remains as is. Final Answer: \[ \boxed{\text{The expression cannot be simplified further.}} \]
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