Back To Course

ELM: CSU Math Study Guide17 chapters | 147 lessons | 7 flashcard sets

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Jennifer Beddoe*

Inverse operations are mathematical operations that undo each other. The square root is the inverse of the squared (or multiplying a number by itself) operation. There is an easy method for estimating the square root of a number, which you will learn in this lesson.

In mathematics, the square root operation is the opposite of squaring a number. To **square** a number, you multiply that number by itself. To find the **square root** of a number, you need to find the number that when multiplied by itself equals the original number. The symbol for square root looks like this:

A **perfect square root** is a number whose square root is an integer. An **integer** is a number that is not a fraction or a decimal. For example, the square root of 25 is equal to 5 because 5^2 is 25, and the square root of 121 is equal to 11 because 11^2 is 121.

A number whose square root is not an integer is an **imperfect square**. When finding the square root of these numbers, the answer will not be an integer, but will be a fraction or decimal. For example, the square root of 27 is equal to 5.196, and the square root of 215 is equal to 14 2/3.

To determine the square root of an imperfect square, you can use a calculator. However, you can also estimate the square root of a number.

Here are the steps to estimating the square root of a number to two decimal places:

Step One - Determine which two perfect squares your number falls between. The answer you are looking for will fall between these two numbers.

Step Two - Take a guess about the number just after the decimal place.

Step Three - Divide the number whose square root you are trying to determine by your guess.

Step Four - Find the average between your guess and the answer to the division problem you did in Step Three.

And lastly, Step Five - Repeat Steps Three and Four until the two numbers you are averaging are the same.

Let's do a few examples; that should help everything make sense:

Estimate the square root of 10 to two decimal places.

Step One - The square root of 9 is equal to 3, and the square root of 16 is equal to 4, so our answer to the square root of 10 will be between 3 and 4.

Step Two - 10 is much closer to 9 than it is to 16, so my first guess on the answer will be 3.2.

For Step Three, I divide 10 by the guess of 3.2, which gives a result of 3.13.

For Step Four, I take the average of 3.2 and 3.13, and I get 3.17.

Now, for Step Five, I repeat Step Three with 3.17. 10 divided by 3.17 is equal to 3.15.

And, then I average 3.17 and 3.15 to get 3.16.

Going back again to Step Three, I divide my original number 10 by my latest average of 3.16, and when I do that, I get 3.16 again. Because this division gives us the same result, our estimation is finished, and the answer to our problem of 'what is the square root of 10' is 3.16.

Try this second example for yourself:

Estimate the square root of 22 to two decimal places.

Did you get an answer of 4.69? If you did, great! If not, don't despair. Here are the steps we took to get there:

When I solved this problem, my first guess was 4.5 because 22 is between 16, which is 4^2, and 25, which is 5^2.

Next, I divided 22 by 4.5 to get 4.89.

Then, I took the average of 4.5 and 4.89 to get 4.70.

Going back and dividing 22 by 4.70, I got 4.68.

Then, the average of 4.70 and 4.68 is 4.69.

When you divide 22 by 4.69 you get 4.69.

Therefore, the answer to the question, 'what is the square root of 22' is 4.69. Remember, you can always check your answer either on a scientific calculator or by multiplying your answer by itself and see if you end up with the original number.

Not all numbers have **perfect square roots**; some are imperfect, containing fractions or decimals. You can estimate the **imperfect square** root of a number using a guess and check method. It can be used on both small and large numbers. It is fairly quick and can be done using just some simple math.

You'll be able to estimate the imperfect square root of numbers using a step-by-step approach after watching this video lesson.

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Login here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
2 in chapter 4 of the course:

Back To Course

ELM: CSU Math Study Guide17 chapters | 147 lessons | 7 flashcard sets

- Introduction to HTML & CSS
- Introduction to JavaScript
- Computer Science 332: Cybersecurity Policies and Management
- Introduction to SQL
- Computer Science 203: Defensive Security
- JavaScript Language Basics
- Error Handling, Debugging & Events in JavaScript
- HTML Elements & Lists
- Conditionals, Arrays & Loops in JavaScript
- Introduction to HTML
- Anti-Bullying Survey Finds Teachers Lack the Support They Need
- What is the ASCP Exam?
- ASCPI vs ASCP
- MEGA Exam Registration Information
- MEGA & MoGEA Prep Product Comparison
- PERT Prep Product Comparison
- MTLE Prep Product Comparison

- Simple Scientific Tools & Uses for Kids
- Chi Square Distribution: Definition & Examples
- Stars: Definition & Facts
- Linear Approximations Using Differentials: Definition & Examples
- Access Control: Types & Implementation
- 'I Am' Poem Lesson Plan
- Key Controls in Cybersecurity Risk Management: Definition & Use
- Quiz & Worksheet - Line Integrals
- Quiz & Worksheet - Frankenstein Creature Quotes
- Quiz & Worksheet - A Christmas Carol Facts
- Quiz & Worksheet - Preschool Classroom Technology
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- Analytical Essay Topics for Teachers
- 8th Grade Math Worksheets

- High School Geometry: Help and Review
- CSET English Subtest II (106): Practice & Study Guide
- Environmental Science 101: Environment and Humanity
- Amsco Geometry: Online Textbook Help
- Accounting 101: Financial Accounting
- Celestial Orbit Characteristics
- MTTC Math (Secondary): Perimeter & Area
- Quiz & Worksheet - Calculating Osmolality
- Quiz & Worksheet - Characteristics of Tissues
- Quiz & Worksheet - Characteristics & Types of Diuretics
- Quiz & Worksheet - Hemoptysis Causes & Treatment
- Quiz & Worksheet - Light and Relativity

- Space Contraction: Shortening Distance for Fast Moving Objects
- Frustrated Total Internal Reflection
- Layers of the Earth Project Ideas
- Education Advocacy Groups & Organizations
- Curriculum Development Templates
- Algebra Math Games
- 9th Grade Reading List
- How to Pass the CCRN Exam
- New York State (NYS) Common Core Standards
- 100th Day of School Project Ideas
- Sarasota Adult Education
- Is the TAP Test Hard?

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject