Question

Simplify. $$\frac{\sqrt{40 x^{5} y^{2}}}{\sqrt{5 x y}}$$

   Simplify.
$$\frac{\sqrt{40 x^{5} y^{2}}}{\sqrt{5 x y}}$$

Prealgebra and Introductory Algebra

Prealgebra and Introductory Algebra

Richard N. Aufmann,… 3rd Edition

Chapter 15, Problem 56

Instant Answer

Solved by Expert Amy Jiang

06/23/2020

Step 1

Step 1: First, we can rewrite the expression inside the square root in the numerator as follows: $$\frac{\sqrt{40 x^{5} y^{2}}}{\sqrt{5 x y}} = \frac{\sqrt{5 \cdot 8 \cdot x^{4} \cdot x \cdot y^{2}}}{\sqrt{5 x y}}$$ Show more…

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Simplify. $$\frac{\sqrt{40 x^{5} y^{2}}}{\sqrt{5 x y}}$$

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Key Concepts

Properties of Square Roots

This concept involves understanding how to combine and separate square roots using the product and quotient rules. For example, the identity ?a/?b = ?(a/b) allows for combining the radicals into one expression, which is a common step in simplification.

Factorization Under Radicals

This concept is about breaking down the expression inside a radical into factors, particularly identifying perfect square factors. Recognizing and extracting these perfect squares simplifies the radical expression by moving factors outside the square root.

Exponent Rules in Radicals

This involves applying the laws of exponents to expressions under a radical sign. It includes handling powers of variables by rewriting them as products of squares and remaining factors, which facilitates the extraction of perfect square factors from beneath the radical.

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