Question

Rationalize the denominator. $\frac{\sqrt{2}}{\sqrt{5}}$

   Rationalize the denominator.
$\frac{\sqrt{2}}{\sqrt{5}}$

Precalculus

Robert Blitzer 5th Edition

Chapter 0, Problem 47

Instant Answer

Solved by Expert Natalie Anderson

03/16/2020

Step 1

This is possible because multiplying by $\sqrt{5}$ over $\sqrt{5}$ is essentially multiplying by 1, which does not change the value of the fraction. So, we get $\frac{\sqrt{2}*\sqrt{5}}{\sqrt{5}*\sqrt{5}}$. Show more…

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Rationalize the denominator. $\frac{\sqrt{2}}{\sqrt{5}}$

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Key Concepts

Rationalization

This is the process of eliminating irrational numbers, such as square roots, from the denominator of a fraction. It involves multiplying the numerator and the denominator by an appropriate expression that will result in a rational number in the denominator.

Multiplication Property of Radicals

This property states that the product of two square roots is equal to the square root of the product of the two numbers (i.e., ?a * ?b = ?(ab)). It is fundamental when rationalizing denominators where a radical is removed by multiplying by a conjugate or a simple radical factor.

Simplification of Radical Expressions

After performing operations like multiplication of radicals, it is often necessary to simplify the resulting expression. This involves combining like terms and reducing the expression to its simplest form, which is an important step in ensuring clarity and precision in the final answer.

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