Question

Simplify. Assume that $x \geq 0$ $\sqrt[4]{25}$

   Simplify. Assume that $x \geq 0$
$\sqrt[4]{25}$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Margaret L. Lial,… 7th Edition

Chapter 10, Problem 105

Instant Answer

Solved by Expert Nick Johnson

02/11/2022

Step 1

We can write 25 as $5^2$. So, we have $\sqrt[4]{5^2}$. Show more…

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Simplify. Assume that $x \geq 0$ $\sqrt[4]{25}$

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Key Concepts

Simplification of Radicals

The process of simplifying radicals includes identifying and extracting perfect power factors from the radicand. In expressions like the fourth root of a number that itself is a perfect square, the number can often be rewritten to reveal relationships between the exponent and the radical's index, aiding in reducing the expression to a simpler form.

Radical Expressions

Radical expressions involve the use of roots, such as square roots, cube roots, or fourth roots, to represent the inverse of exponentiation. They are fundamental to algebra and are often simplified by rewriting the radicand as a product of factors, some of which may be perfect powers matching the index of the radical.

Rational Exponents

Rational exponents offer an alternate way to express radical operations by writing roots as fractional powers. For example, representing a fourth root as raising a number to the power of ¼ enables easier manipulation of expressions using the laws of exponents.

Even Roots and Principal Values

Even roots, like the square root or fourth root, are defined to return nonnegative values for nonnegative radicands. This adherence to principal values ensures that the functions are well-defined and single-valued, which is why assumptions such as x ? 0 often appear in problems involving these roots.

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