Question

Simplify each expression. $-\sqrt{100 x^{6}}$

   Simplify each expression.
$-\sqrt{100 x^{6}}$

Intermediate Algebra for College Students

Intermediate Algebra for College Students

Robert Blitzer 7th Edition

Chapter 7, Problem 41

Instant Answer

Solved by Expert Amy Jiang

06/06/2020

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First, we can simplify the square root of 100, which is 10. Show more…

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Simplify each expression. $-\sqrt{100 x^{6}}$

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Key Concepts

Radical Simplification

This concept involves rewriting expressions under a square root by factoring out perfect squares. It includes using the property that the square root of a product is the product of the square roots, which allows one to simplify the radicand by extracting factors whose square roots are known.

Exponent Rules

This concept covers the manipulation of powers and roots, such as understanding that taking the square root of a variable raised to an even power leads to extracting half the exponent. The rules of exponents simplify expressions by allowing the conversion of radical notation to exponential notation.

Absolute Value in Radical Simplification

When simplifying even-powered variables under a square root, it is necessary to incorporate the absolute value. This is because the square root operation yields the non-negative principal square root, ensuring the simplified expression remains valid for all real inputs.

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