Question

Simplify the radical expressions. $$\sqrt{\frac{x^{3}}{x}}$$

Name: Problem 33, Chapter 6: Intermediate Algebra
Uploaded: 2020-06-21T06:45:12-08:00
Duration: 23 s
Channel: Ankit Gupta
Description: Simplify the radical expressions. √((x^3)/(x))

   Simplify the radical expressions. $$\sqrt{\frac{x^{3}}{x}}$$

Intermediate Algebra

Julie Miller, Molly… 5th Edition

Chapter 6, Problem 33

Instant Answer

Solved by Expert Ankit Gupta

06/21/2020

Step 1

We have $\frac{x^{3}}{x}$ which simplifies to $x^{2}$ because when we divide exponents with the same base, we subtract the exponents. So, $3 - 1 = 2$. Show more…

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Simplify the radical expressions. $$\sqrt{\frac{x^{3}}{x}}$$

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Key Concepts

Properties of Radicals

One important property of radicals is that the square root of a square, ?(a²), equals the absolute value of a. This is used to simplify expressions inside a radical when they involve even exponents.

Absolute Value

The absolute value function ensures that the outcome of an expression is non-negative. When simplifying a square root of a squared variable, replacing it with the absolute value maintains the correct behavior for all real numbers.

Exponent Rules

When dividing expressions with the same base, subtract the exponents. This rule simplifies expressions such as x³/x to x^(3-1), which provides a clearer form within the radical.

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