Combine the radicals using addition and subtraction, if possible.

Question

9√26 − 5√6 + 3√54=

22√6

4√6

Unlike radicals cannot be combined using addition and subtraction.

42√2

Answer 1

Let's simplify the expression \(9\sqrt{26} - 5\sqrt{6} + 3\sqrt{54}\) step by step.

1. Simplify \(3\sqrt{54}\): \[ \sqrt{54} = \sqrt{9 \times 6} = \sqrt{9} \times \sqrt{6} = 3\sqrt{6} \] So, \[ 3\sqrt{54} = 3 \times 3\sqrt{6} = 9\sqrt{6} \]

2. Substitute back into the expression: \[ 9\sqrt{26} - 5\sqrt{6} + 9\sqrt{6} \]

3. Combine like terms: Combine \(-5\sqrt{6}\) and \(9\sqrt{6}\): \[ -5\sqrt{6} + 9\sqrt{6} = (9 - 5)\sqrt{6} = 4\sqrt{6} \]

4. Final expression: The expression now becomes: \[ 9\sqrt{26} + 4\sqrt{6} \]

Since \(9\sqrt{26}\) and \(4\sqrt{6}\) are unlike radicals, they cannot be combined further. Thus, the final simplified expression is:

\[ 9\sqrt{26} + 4\sqrt{6} \]

To answer your initial question regarding combining radicals, the correct choice is:

• Unlike radicals cannot be combined using addition and subtraction.