Question

What is the simplified radical form of √221?

Answer 1

The simplified radical form of √221 is
`\( √(221) = √(13 * 17) \)`.

Step-by-step explanation

The expression
`\( √(221) \)` can be simplified by breaking down the number 221 into its prime factors. Prime factorization reveals that 221 is the product of 13 and 17. Therefore,
`\( √(221) \)` can be expressed as
`\( √(13 * 17) \)`. The square root of a product is equal to the product of the square roots of the individual factors. Hence,
`\( √(221) = √(13) * √(17) \)`
`\( √(221) = √(13) * √(17) \)`. However, since neither 13 nor 17 has perfect square roots, the radical cannot be further simplified into whole numbers. Therefore, the simplified radical form of
`\( √(221) \)` remains
`\( √(13 * 17) \)`.

Breaking down the square root into prime factors aids in simplifying radicals, as it allows us to identify perfect squares that can be taken out of the radical. In this case,
`\( √(13 * 17) \)` is the most simplified form, as neither 13 nor 17 has perfect square roots. Attempting to simplify further would result in irrational numbers and defeat the purpose of finding the simplified radical form. In conclusion,
`\( √(13 * 17) \)` can be expressed most simply as
`\( √(13 * 17) \)`, providing a clear and concise representation of the radical expression.