/*! 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 8 Solve the given equation. $$\s... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 8

Solve the given equation. $$\sqrt{u}=8$$

Short Answer

Expert verified
u = 64

Step by step solution

01

Identify the Equation

The given equation is \(\sqrt{u} = 8\).
02

Square Both Sides

To eliminate the square root, square both sides of the equation: \( (\sqrt{u})^2 = 8^2 \).
03

Simplify the Equation

Simplify the squared terms: \(u = 64 \).

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.

Understanding Square Root
The square root is a fundamental concept in mathematics, symbolized by the radical sign \( \sqrt{...} \). It represents a value that, when multiplied by itself, gives the original number. For example, the square root of 64 is 8 because \( 8 \times 8 = 64 \). In our exercise, we start with the equation \( \sqrt{u} = 8 \). Here, \( u \) is the number under the square root that we need to figure out. The goal is to remove the square root to solve for \( u \). This leads us to our next concept, squaring both sides.
Squaring Both Sides
Squaring both sides is an effective method to eliminate the square root from an equation. To 'square' a number simply means to multiply it by itself. For example, \( 8^2 = 8 \times 8 = 64 \). In our exercise, after identifying that we have \( \sqrt{u} = 8 \), we square both the left and right sides of the equation. The process involves:
  • Squaring the left side: \( (\sqrt{u})^2 = u \)
  • Squaring the right side: \( 8^2 = 64 \)
This results in the simplified equation \( u = 64 \) with the square root no longer present, making it easier to solve.
Simplification
Simplification is an essential skill in equation solving. The goal is to reduce the equation to its simplest form, making it easier to solve. In our example, after squaring both sides of the equation, we ended up with \( u = 64 \). This means we have simplified the original problem to its basic result. Simplification involves performing operations like:
  • Combining like terms
  • Eliminating unnecessary components (e.g., removing the square root by squaring)
  • Ensuring the equation is in its most straightforward form
By following these steps, we obtain our final solution: \( u = 64 \).

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

Perform the indicated operations. Simplify all answers as completely as possible. Assume that all variables appearing under radical signs are nonnegative. $$\frac{12}{3+\sqrt{5}}$$

Perform the indicated operations and simplify. $$\frac{3}{2 x}+\frac{5}{x+2}$$

Perform the indicated operations. Simplify all answers as completely as possible. Assume that all variables appearing under radical signs are nonnegative. $$\frac{\sqrt{3}}{2+\sqrt{3}}$$

In each of the following, perform the indicated operations and simplify as completely as possible. Assume all variables appearing under radical signs are non negative. $$\sqrt{20 y^{3}}-\sqrt{45 y^{3}}$$

Solve the following problems algebraically. Be sure to label what the variable represents. An orchestral society put on a concert. The members sold 200 tickets in advance and 75 tickets at the door. They charged \(\$ 1.50\) more for tickets at the door than for advance-sale tickets. If they collected a total of \(\$ 1,075,\) how much did they charge for tickets at the door?
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

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.