How Do You Simplify Radicals Using the Product Property?

How Do You Simplify Radicals Using the Product Property?

Note:

Want to simplify a radical whose radicand is not a perfect square? No sweat! Check out this tutorial and see how to write that radicand as its prime factorization. Then, rewrite any duplicate factors using exponents, break up the radical using the product property of square roots, and simplify. To see this process step-by-step, watch this tutorial!

Keywords:

  • problem
  • simplify
  • radical
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  • simplify radicals
  • root
  • square root
  • product property
  • product property of square roots
  • square
  • factor
  • factorization
  • prime factorization
  • prime
  • radicand
  • perfect square
  • exponent
  • exponents
  • simplest radical form
  • simplest form

Background Tutorials

  • Powers and Exponents

      • What are Exponents?What are Exponents?

      What are Exponents?

      Did you know that another word for 'exponent' is 'power'? To learn the meaning of these words and to see some special cases involving exponents, check out this tutorial!

  • Square Roots

      • How Do You Find the Square Root of a Perfect Square?How Do You Find the Square Root of a Perfect Square?

      How Do You Find the Square Root of a Perfect Square?

      Taking the square root of a perfect square always gives you an integer. This tutorial shows you how to take the square root of 36. When you finish watching this tutorial, try taking the square root of other perfect squares like 4, 9, 25, and 144.

      • What's a Perfect Square?What's a Perfect Square?

      What's a Perfect Square?

      Anytime you square an integer, the result is a perfect square! The numbers 4, 9, 16, and 25 are just a few perfect squares, but there are infinitely more! Check out this tutorial, and then see if you can find some more perfect squares!

  • Factors

      • How Do You Find the Prime Factorization of a Number Using a Tree?How Do You Find the Prime Factorization of a Number Using a Tree?

      How Do You Find the Prime Factorization of a Number Using a Tree?

      To write the prime factorization for a number, it's often useful to use something called a factor tree. Follow along with this tutorial and see how to use a factor tree to find the prime factorization of a given number.

      • What's a Factor?What's a Factor?

      What's a Factor?

      Factors are a fundamental part of algebra, so it would be a great idea to know all about them. This tutorial can help! Take a look!

  • Multiplying and Dividing Radicals

      • What is the Product Property of Square Roots?What is the Product Property of Square Roots?

      What is the Product Property of Square Roots?

      The product property of square roots is really helpful when you're simplifying radicals. This property lets you take a square root of a product of numbers and break up the radical into the product of separate square roots. Check out this tutorial and learn about the product property of square roots!