Question

Express each radical in simplified form. $$ -\sqrt[4]{1250} $$

   Express each radical in simplified form.
$$
-\sqrt[4]{1250}
$$

Intermediate Algebra

Intermediate Algebra

Margaret L. Lial,… 11th Edition

Chapter 8, Problem 54

Instant Answer

Solved by Expert Amy Jiang

07/25/2020

Step 1

We can do this by dividing 1250 by the smallest prime number, which is 2, and continue dividing the quotient by the smallest possible prime number until we are left with only prime numbers. Show more…

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Express each radical in simplified form. $$ -\sqrt[4]{1250} $$

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Key Concepts

Radical Expressions

Radical expressions involve the notation that represents roots, such as square roots, cube roots, and in this case, fourth roots. Understanding radical expressions means recognizing that the radical symbol denotes an operation that finds a number which, when raised to a specific power (the index), equals the radicand.

Simplification of Radicals

Simplifying a radical requires factoring the radicand into a product of factors, identifying any perfect power factors that match the radical’s index. These perfect power factors can be taken out of the radical, thus simplifying the overall expression.

Extraction of Perfect Powers

Extraction of perfect powers is the process of identifying portions of the radicand that are exact powers corresponding to the radical’s index. Once these parts are factored out, they are replaced by their corresponding base raised to the appropriate power outside the radical, making the expression easier to work with.

Relationship Between Radicals and Exponents

Radicals and exponents are closely related, as a radical can be expressed as a rational exponent. For example, the nth root of a number is equivalent to raising that number to the 1/n power. This connection is useful for simplifying radical expressions and applying exponent rules during the simplification process.

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