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How do you know when a radical expression is in simplest form?

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Final answer:

A radical expression is in simplest form when all perfect square factors are eliminated from the radicand, the expression inside the radical is at its smallest non-divisible form, and no radicals are in the denominator of a fraction.

Step-by-step explanation:

A radical expression is in simplest form when several key steps have been followed:

  • Ensure no perfect square factors remain within the radical.
  • Simplify the radicand, which is the number or expression inside the radical, to its smallest components.
  • Any terms outside the radical should be simplified by combining like terms.
  • Verify that no fraction exists within the radicand nor should there be any radicals in the denominator of a fraction.

Using algebra to eliminate terms wherever possible helps in simplifying the expression.

For example, an expression like √(x²) would simplify to x because squaring x and taking the square root cancels each other out.

After simplification, always check the answer to see if it makes sense and no further simplification is possible.

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