Square Root Radical Form

 "Roots" are the "conflicting" progression of apprehension exponents or in other words “Radicals are the opposite operations of an exponent”; you can "unwrap" a power (degree) with a radical, and a radical can "unwrap" a power (degree). The expression sqrt25 can also be called as square root of 25 or root of 25. For incidence, if we squared a value of 9, you get 81, and if you "take the square root of 81", you obtain 9; if you square 8, you obtain 64, and if you "take the square root of 64", you obtain 8.

 

Example for Square Root Radical Form:

 

Example for Square roots Radicals form 1:

       Simplify the radical:    `sqrt (25) / (sqrt16)`  

             Step 1: Factors of 25 = 5 × 5 

                                  `sqrt (25) = sqrt (5 xx 5)`

                                             `= sqrt5^2`

             Step 2: Square root of `5^2 = 5` ;                we know `rootn (x^n) = x`   , here n = 2

             Step 3: Factors of 16 = 4 × 4

                          `sqrt (16) = sqrt (4 xx 4) = sqrt4^2`        

             Step 4:  `sqrt4^2 =4` ;                                    we know `rootn (x^n) = x`   , here n = 2

             Step 5: so, `sqrt (25) / sqrt16)`  = `5 / 4`        

          Answer for the given square roots radicals is `5 / 4`  

 

Example for Square roots Radicals form 2:

 

       Simplify the given square roots radical form:    `sqrt (64) / (sqrt81)`  

             Step 1: Factors of 81 = 9 × 9 

                                  `sqrt (81) = sqrt (9 xx 9)`

                                             `= sqrt9^2`

             Step 2: Square root of 92 = 9;              we know `rootn (x^n) = x`   , here n = 2         

            Step 3: Factors of 64 = 8 × 8

                          `sqrt (64) = sqrt (8 xx 8) = sqrt8^2`       

             Step 4:  `sqrt8^2 =8 ` ;                                 we know `rootn (x^n) = x `   , here n = 2

             Step 5: so, `sqrt (81) / sqrt64`  = `9 / 8`        

          Answer for the given square roots radicals is `9 / 8`  

 

Example for Square roots Radicals form 3:

 

       Simplify the given square roots radical form:    `sqrt (169) / sqrt (324)`  

             Step 1: Factors of 169 = 13 × 13 

                                  `sqrt (169) = sqrt (13 xx 13)`

                                             `= sqrt132`

             Step 2: Square root of 132 = 13;               we know `rootn (x^n) = x `   , here n = 2

             Step 3: Factors of 324 = 18 × 18

                          `sqrt (324) = sqrt (18 xx 18) = sqrt18^2`       

             Step 4:  `sqrt18^2 =18` ;                                   we know `rootn (x^n) = x`   , here n = 2            

            Step 5: so, `sqrt (169) / sqrt (324)`  = `13 / 18 `        

          Answer for the given square roots radicals is `13 / 18 `

 

Practice Problem for Square Roots Radicals Form:

 

Practice problem for Square roots Radicals form 1:

Simplify the square roots radicals:    `sqrt (25) / (sqrt81)`

Answer :`( 5/9)`

Practice problem for Square roots Radicals form 1:

Simplify the square roots radicals:    `sqrt (64) / (sqrt100)`

Answer :`( 8/10)`

Practice problem for Square roots Radicals form 1:

Simplify the square roots radicals:    `sqrt (49) / (sqrt144)`  

Answer :`( 7/12)`