Radical Expressions Solver

Introduction radical expressions:

             The word radical was used to refer to an irrational number. The meaning of the radical is “ROOT”.  A radical is an expression that expresses the square roots, cube roots etc. Radical is the word that comes from the Latin word Radix. When we use the radical without a sign or index number, it mentions the positive square root of the radical. Radicals having the same properties as the properties of the numbers.

Definition of Radical Expressions:

            A Radical Expression is an expression which contains a square root,cubic root and n^th root

Examples:-

           are examples of radical expression.

Identities and properties:

   Multiplication property  for radical expression:        `root(n)(ab)` =  `root(n)(a)`  `root(n)(b)`

   Division property for radical expression:         `root(n)((a / b))`  = `root(n)(a)`  / `root(n)(b)`

General expression with exponent and radical:

   `root(n)(a)`^m   =  (`root(n)(a)`)^m   =  (a^1/n )^m = a^m/n                          

Solved Examples on Radical Expression:

Radical Expression Solver Example 1. Evaluate the Radical expression:  √12

       Solution:

                    √12 = √ (4×3)

                             = √4 × √3

                             = 2 √3

       Answer:  2 √3

Radical Expression Solver Example 2. Multiply the radical expression: √3x²and √5x

      Solution:

                          √3x² × √5x = x√ (3×5x)

                                               = x√15x

      Answer: x√15x

Radical Expression Solver Example 3. Divide the radical expression:  √16 / √4

       Solution:  

         √16 / √4     = (√4 × √4) / √ 4

                             = √4 

                              = 2

       Answer: 2 

Radical Expression Solver Example 4. Simplify the radical expression:  9√25 / 45

        Solution: 

                               9√25 / 45 = (9 × √25) / 45

                                               = (9 ×5) / 45

                                               = 45 / 45

                                               = 1

        Answer: 1

Radical Expression Solver Example 5. Solve the radical expression: (√ 8x³) (3√15 x⁴) 

        Solution:

                  √ 8x³ × 3√15x⁴ = (√ (2×4x³) × 3√15x⁴)

                                              = ((2x√ 2x) (3x²√15))

                                              = 6x³ √30x

        Answer: 6x³ √30x

Radical Expression Solver Example 6. Multiply the radical expression:  (3√9) and (√27)

       Solution:

                          (3√9) (√27) = 3 × √ (3 × 3) × √ (3 × 3 ×3)

                                                = 3 × 3 × 3√3

                                                = 27√3

       Answer: 27√3

Radical Expression Solver Example 7. Solve the radical expression:  √ (a⁴b²) = √ (a^{2 ×} a² × b² )

       Solution:                         

                      √ (a⁴b²) = √ (a² × a² × b²)

                                      = a² × b

                                      = a² b

       Answer: a² b

Radical Expression Solver Example 8. Solve the radical expression:   √ (18x⁵y⁴z)

      Solution:

                          √ (18x⁵y⁴z)   =    √ (2× 9 × x⁵ × y⁴ × z) 

                                                 = 3 x²y²√ (2xz)

       Answer: 3 x²y²√ (2xz)

Radical Expression Solver Example 9. Solve the radical expression:   2√56 × 9√25

       Solution:

                2√56 × 9√25 =  2(√2×4×7) 9√25)

                                        = 2×2(√14) 9×5

                                       = 180 √14

       Answer: 180 √14

Radical Expression Solver Example 10. Solve  the radical expression: √256 / √81

       Solution:

                    √256 / √81 = √ (16×16) / √ (9×9)

                                        = 16 / 9

       Answer: 16 / 9