/*! 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 51 Simplify. $$\sqrt{8 h}+\sqrt{3... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 51

Simplify. $$\sqrt{8 h}+\sqrt{32 h}$$

Short Answer

Expert verified
\( 6\sqrt{2h} \)

Step by step solution

01

Identify the Expression

Given the expression is \( \sqrt{8h} + \sqrt{32h} \)
02

Simplify Each Square Root

Simplify the square root of each term separately. \( \sqrt{8h} = \sqrt{4 \cdot 2 \cdot h} = \sqrt{4} \cdot \sqrt{2h} = 2\sqrt{2h} \) and \( \sqrt{32h} = \sqrt{16 \cdot 2 \cdot h} = \sqrt{16} \cdot \sqrt{2h} = 4\sqrt{2h} \)
03

Combine Like Terms

Now, combine the simplified terms: \( 2\sqrt{2h} + 4\sqrt{2h} = (2 + 4)\sqrt{2h} = 6\sqrt{2h} \)

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Square Roots
Square roots help find a number that, when multiplied by itself, gives you the original number. For example, the square root of 9 is 3, because 3 * 3 = 9.

When dealing with variables, find the square root of any perfect squares within the expression first.

In our exercise, we have to simplify the square roots in the expression: \( \sqrt{8h} + \sqrt{32h} \).

Here's how to do this step by step:
  • Factor each number under the square root into prime factors.
  • Find squares within the factors.
  • Take the square root of these squares out of the radical.
Like Terms
When simplifying expressions, it's important to combine like terms. Like terms are those terms in an expression that have the same variables raised to the same power.

In our exercise, after simplifying the square roots, we found: \( \sqrt{8h} = 2\sqrt{2h} \) and \( \sqrt{32h} = 4\sqrt{2h} \).

Both of these have \( \sqrt{2h} \) as their radicand (the term under the square root).
  • Identify terms with the same radical expression.
  • Combine their coefficients.
This results in a simpler expression.
Radical Simplification
Radical simplification is the process of breaking down a radical expression into its simplest form.

First, you simplify any square roots by factoring out perfect squares.

Next, you identify and combine like terms.

In our example, we start with \( \sqrt{8h} + \sqrt{32h} \):
  • Simplify \( \sqrt{8h} \) to \( 2\sqrt{2h} \).
  • Simplify \( \sqrt{32h} \) to \( 4\sqrt{2h} \).
  • Combine the like terms: \( 2 \sqrt{2h} + 4 \sqrt{2h} = 6 \sqrt{2h} \).
This leaves us with the simplified expression \( 6\sqrt{2h} \).

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

Describe what you think is the difference between teaching and tutoring.

Rewrite the radical expression in exponential notation. $$\sqrt{x^{3}}$$

Simplify. $$\sqrt[4]{8} \sqrt[4]{14}$$

Evaluate. $$\sqrt[3]{-27}$$

Simplify. $$\frac{x^{\frac{4}{5}}}{x^{\frac{1}{5}}}$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

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.