MODULE 5

• DISCIPLINE • GOOD TASTE • EXCELLENCE
• Writer: Chonalyn L. Tecson
• Cover Illustrator: Joel J. Estudillo
• MATHEMATICS Quarter 2: Module 5 Laws of Radicals
• Department of Education National Capital Region SCHOOLS DIVISION OFFICE MARIKINA CITY
• Hello, Grade, 9 learners! In this module, you will learn how to
• You can say that you have understood the lesson in this module if you can already: 1. Derive the laws of radicals from the laws of rational exponents 2. Give the laws of radicals,
• Read each item carefully. Encircle the letter that corresponds to the correct answer.
• √7 • 3^5

  Radical expression
• Possible answers

  • √7^5 + √3^5
  • √7^5/√3^5
  • √7^5 - √3^5
  • √7^5 • √3^5
• √√1000^5 3

  Nested radical expression
• √225^5

  Radical expression
• Possible answers

  • 5
  • 220
  • 225
  • 230
• √√143^3 4

  Nested radical expression
• Possible ways to write it

  • √√143^4 3
  • √143^7
• √7^(1/5 16)

  Radical expression
• Possible answers


  • √7^5 + √16^5
  • √7^5/√16^5
  • √7^5 - √16^5
  • √7^5 • √16^5
• 3^(1/2) in radicals is √3
• √4^(1/3) in an expression with rational exponent is 4^(1/3)
• The equation 5^(2/3) = √5^3 is correct
• It is a common knowledge that rules, or laws are created for a common good. Failure to do so, constitutes unfavorable consequences.
• In learning Mathematics, specifically in working with radicals, it is important that you are familiar with the laws with it. If you would not master laws of radicals, it may result to invalid answers or wrong result in working with it.
• Deriving the laws of radicals


  1. √a^x/x = a

  2. √ab^x = √a^x • √b^x

  3. √a/b^x = √a^x/√b^x

  4. √√a^m n = √a^mn = √√a^n m
• Applying the laws of radicals

  • √124^4 = 12
  • √305^5 = 30
  • √10^7 = √2^7 • √5^7
  • √8^3 = √2^3 • √4^3
• Applying the laws of radicals

  • √13^(2/9) = √13^9/√25^9
  • √√23^6 5 = √23^30 = √√23^5 6
• The brochure will be posted in the class face book page that aims to help learners better understand the derivation of the law of radicals.
• The target audiences are all Grade 9 students in you school who are members of the face book page of their respective classes and others.
• The Mathematics Department is launching a simple math virtual gathering of all Grade 9 students. One of the activities in the said event is the brochure making contest about the lesson Laws of Radicals.
• Laws of radicals

  Derivation of the laws of radicals
• Brochure making


  1. Journal on the process of deriving laws of radicals using laws of exponents

  2. Include pictures, drawings and math clips about laws of radicals

  3. Add other information, figures, and illustration related to the derivation of the laws of radicals
• The knowledge of the derivation of the law of radicals is useful in dealing with real-life situations