Rules of Exponents:
Introduction to Roots
Just as multiplication and division are opposites of each other (example: \(3 \times 5 = 15\) so \(15 \div 5 = 3)\), powers and roots are opposite. Because 5 raised to the 2 power = 25, the 2 root of 25 = 5. Roots can be significantly more difficult to find than powers because not every number has a simple root. To illustrate, \(3^2=9\) means the square root of 9 is 3. Similarly, \(4^2=16\) which means the square root of 16 is 4. But the numbers in between 9 and 16 don’t have a whole number square root because their roots must be somewhere between 3 and 4. Often we solve for roots using a calculator. The following video will help you learn how to solve for roots:
Real World Application
Some calculators have you type the number in first and then hit the square root button. Other calculators may have you do it the opposite way, by selecting the square root button and then typing in the number you want to root. You should experiment with your calculator on a simple square root, such as \(\sqrt{9}=3\), in order to see how your calculator works.
Video Source (05:44 mins) | Transcript
It’s helpful to learn which numbers are “perfect squares”, or the numbers that have whole number roots. These are the numbers that appear on the diagonal of a multiplication table because they are the result of any number being multiplied to itself. Some of these numbers include 4,9,16,25,36,49,64. We highly recommend that you memorize your multiplication facts to help you remember the perfect squares and their roots.
Additional Resources
- Khan Academy: Intro to Square Roots (05:23 mins, Transcript)
- Khan Academy: Understanding Square Roots (01:20 mins, Transcript)
Practice Problems
Evaluate the following expressions:
- \(\sqrt{64}=\)
- \(\sqrt{49}=\)
- \(\sqrt{121}=\)
- \(\sqrt{7}=\)
- \(\sqrt{78}=\)
