/*! 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 122 Explain how to add \(\sqrt{3}+\s... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 122

Explain how to add \(\sqrt{3}+\sqrt{12}\)

Short Answer

Expert verified
Therefore, \(\sqrt{3} + \sqrt{12} = 3\sqrt{3}\)

Step by step solution

01

Simplify the Square Roots

Firstly, simplify \( \sqrt{12} \) as it can be reduced to a more simple form. The number 12 can be expressed as the product of 4 and 3 where 4 is a perfect square. Therefore, \( \sqrt{12} \) can be expressed as: \[ \sqrt{12} = \sqrt{4 x 3} \] Then, we distribute the square root as follows:\[ \sqrt{12} = \sqrt{4} x \sqrt{3} = 2\sqrt{3} \]
02

Perform the Addition

After the simplification, the equation becomes: \[ \sqrt{3} + 2\sqrt{3} \] Which can be interpreted as the addition of like terms, similary to \(1x + 2x = 3x\). So basically, this translates to: \[ 1\sqrt{3} + 2\sqrt{3} = 3\sqrt{3} \]

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

Find the exact value of \(\sqrt{13+\sqrt{2}+\frac{7}{3+\sqrt{2}}}\) without the use of a calculator.

Exercises \(142-144\) will help you prepare for the material covered in the next section. Simplify and express the answer in descending powers of \(x\) : $$2 x\left(x^{2}+4 x+5\right)+3\left(x^{2}+4 x+5\right)$$

Simplify using properties of exponents. $$\frac{\left(3 y^{\frac{1}{4}}\right)^{3}}{y^{\frac{1}{12}}}$$

Exercises will help you prepare for the material covered in the next section. Evaluate each exponential expression in $$ \frac{x^{30}}{x^{-10}} $$

Simplify by reducing the index of the radical. $$\sqrt[9]{x^{6}}$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Calculus

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.