Simplifying Radical Expressions

• Simplifying radical expression


  Using the laws of radicals
• Perfect square


  • Can be simplified as a factor of a perfect square
• Square root of 8

  • Simplified as 2 square root of 2
• Square root of 12

  • Simplified as 2 square root of 3
• Square root of 18

  • Simplified as 3 square root of 2
• Square root of 20

  • Simplified as 2 square root of 5
• Square root of 24

  • Simplified as 2 square root of 6
• Square root of 27

  • Simplified as 3 square root of 3
• Square root of 28

  • Simplified as 2 square root of 7
• Square root of 32

  • Simplified as 4 square root of 2
• Square root of 40

  • Simplified as 2 square root of 10
• Square root of 44

  • Simplified as 2 square root of 11
• Square root of 45

  • Simplified as 3 square root of 5
• Square root of 48


  • Simplified as 4 square root of 3
• Square root of 50

  • Simplified as 5 square root of 2
• Square root of 52

  • Simplified as 2 square root of 13
• Square root of 54


  • Simplified as 3 square root of 6
• Square root of 56

  • Simplified as 2 square root of 14
• Square root of 60

  • Simplified as 2 square root of 15
• Square root of 63

  • Simplified as 3 square root of 7
• Square root of 68

  • Simplified as 2 square root of 17
• Square root of 72


  • Simplified as 6 square root of 2
• Square root of 75

  • Simplified as 5 square root of 3
• Square root of 76

  • Simplified as 2 square root of 19
• Square root of 80

  • Simplified as 4 square root of 5
• Square root of 84

  • Simplified as 2 square root of 21
• Square root of 88

  • Simplified as 2 square root of 22
• Square root of 90

  • Simplified as 3 square root of 10
• Square root of 92

  • Simplified as 2 square root of 23
• Square root of 96

  • Simplified as 4 square root of 6
• Square root of 98

  • Simplified as 7 square root of 2
• Square root of 99

  • Simplified as 3 square root of 11
• Law: Square root of the product of two non-negative numbers

  Equal to the product of their square roots
• Simplifying radical expression

  1. Express perfect square factors

  2. Remove perfect square factors

  3. Simplify remaining radicand
• Reducing index

  The m-th root of the n-th root of a = the (m*n)-th root of a
• Simplifying square root of x^5

  • x^2 * square root of x
• Simplifying cube root of b^7

  • b^2 * cube root of b
• Simplifying square root of 63m^2


  • 3 * square root of 7 * square root of m
• Simplifying square root of 60x^4y^5

  • 2 * x^2 * y^2 * square root of 15y
• Simplifying cube root of 125x^5y^18

  • 5 * x^(5/3) * y^6