/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 123 Describe what it means to ration... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 123

Describe what it means to rationalize a denominator. Use both \(\frac{1}{\sqrt{5}}\) and \(\frac{1}{5+\sqrt{5}}\) in your explanation.

Short Answer

Expert verified
To rationalize a denominator means to eliminate any irrational numbers present in it through multiplication by a suitable expression. The rationalized denominators for \(\frac{1}{\sqrt{5}}\) and \(\frac{1}{5+\sqrt{5}}\) are \(\frac{\sqrt{5}}{5}\) and \(\frac{5 - \sqrt{5}}{20}\) respectively.

Step by step solution

01

Rationalize the denominator of \(\frac{1}{\sqrt{5}}\)

To rationalize the denominator of \(\frac{1}{\sqrt{5}}\), multiply the numerator and denominator by \(\sqrt{5}\). This gives \(\frac{\sqrt{5}}{5}\).
02

Rationalize the denominator of \(\frac{1}{5+\sqrt{5}}\)

For the expression \(\frac{1}{5+\sqrt{5}}\), the conjugate of the denominator (5 + \(\sqrt{5}\)) is needed. This is obtained by changing the sign in the middle, producing (5 - \(\sqrt{5}\)). Multiply the numerator and the denominator by this conjugate to get \(\frac{5 - \sqrt{5}}{20}\). Rationalizing this expression eliminates the square root from the denominator.
03

Simplify the expressions

Both expressions \(\frac{\sqrt{5}}{5}\) and \(\frac{5 - \sqrt{5}}{20}\) are now rationalized. They may be left as they are or simplified further if possible. In this case, the expressions are already at their simplest form.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

List all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. $$\\{-5,-0 . \overline{3}, 0, \sqrt{2}, \sqrt{4}\\}$$

List all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. $$\left\\{-11,-\frac{5}{6}, 0,0.75, \sqrt{5}, \pi, \sqrt{64}\right\\}$$

Multiply: \(\quad\left(2 x^{3} y^{2}\right)\left(5 x^{4} y^{7}\right)\)

Explain how to factor the difference of two squares. Provide an example with your explanation.

Your computer store is having an incredible sale. The price on one model is reduced by \(40 \% .\) Then the sale price is reduced by another \(40 \% .\) If \(x\) is the computer's original price, the sale price can be modeled by $$(x-0.4 x)-0.4(x-0.4 x)$$ a. Factor out \((x-0.4 x)\) from each term. Then simplify the resulting expression. b. Use the simplified expression from part (a) to answer these questions. With a \(40 \%\) reduction followed by a \(40 \%\) reduction, is the computer selling at \(20 \%\) of its original price? If not, at what percentage of the original price is it selling?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.