Radical Rules Math

Radical symbol used to indicate the square root or nth root. Radical of an algebraic group, a concept in algebraic group theory. Radical of a ring, in ring theory, a branch of mathematics, a radical of a ring is an ideal of "bad" elements of the ring. Radical of a module, in the theory of modules, the radical of a module is a component in the theory of structure and classification. Radical of an ideal, an important concept in abstract algebra. The radical symbol is ' √ ' . The cubic root of a can be expressed as `root(3)(a)`   and nth root of x can be expressed as  ` rootn x `                                                                                                                                                                                                   

                                                                                                                                                                                                                   Source Wikipedia.

I like to share this sine rules with you all through my article. 

Radical rules in math:

                    Math radical has product rule, Division rule and exponential rule.
Math Product rules for radical:
              Square root product rule:         `sqrt(ab)`   =  ` sqrta * sqrt b`
              Cube root product rule:          `root3 (ab) `   = ` root3 (a) * root3 (b)`
              n^th root product rule                ` rootn (ab) = rootn (a) * rootn (b)`
Examples for radical product rule math problem 1:
              Multiply the two math radical `sqrt5 * sqrt14`
        Solution:
                            Given radicals`sqrt5 * sqrt14`        
               We know the math radical product rule  `sqrt(ab)`   =  ` sqrta * sqrt b` 
                                     So, `sqrt5 * sqrt14`  =`sqrt(5 * 14)`
                                                                = `sqrt70`
        Answer: `sqrt70` 
Examples for radical product rule math problem 2:
              Multiply the two math radical `sqrt 18 * sqrt 3`
        Solution:
                            Given radicals `sqrt18 * sqrt3`           
               We know the math radical product rule  `sqrt(ab)`   =  ` sqrta * sqrt b` 
                                     So,  `sqrt18 * sqrt3` =`sqrt(18 * 3)`
                                                                = `sqrt54`
        Answer:  `sqrt54`
Math Division rules for radical:
                Square root division rule:        ` sqrt(a/b)` = `sqrta / sqrt b`
               Cube root division rule:          ` root3 (a/b)` =  `root3 (a) / root3 (b)`
               n^th root division rule                 `rootn (a/b)` = `rootn (a) / rootn (b)`
Examples for radical division rule math problem 1:
              Simplify  the math radical ` root3 (66) / root3 (11)`
       Solution:
                            Given math radicals  ` root3 (66) / root3 (11)`      
               We know the math radical division rule    ` root3 (a/b)` =  `root3 (a) / root3 (b)`
                                                So, ` root3 (66) / root3 (11)`   = `root3 (66/11)`
                                                                      = `root3 6`
        Answer: `root3 6`
Examples for radical division rule math problem 2:
              Simplify  the math radical ` root4 (16) / root4 (24)`
       Solution:
                            Given radicals ` root4 (16) / root4 (24)`      
               We know the math radical division rule    `rootn (a/b)` = `rootn (a) / rootn (b)`
                                              So, ` root4 (16) / root4 (24)`   = `root4 (16/24)`
                                                                      = `root4 (2/3)`
        Answer:  `root4 (2/3)`

Other Radical rules in math:

Relation rules with exponential term:
                      `root(n)(x)`^m =( `root(n)(x)` )^m = (x^1/n )^m = x^m/n
Examples for radical with exponent math problem 1:
              Simplify the math radical `"(root5 4)^5 * `
        Solution:
                     Given math radicals `(root5 4)^5 * (sqrt27)^2`
                                                = `(root5 4)^5 * (sqrt27)^2`
              we know the math radical rule with an exponents  ( `root(n)(x)` )^m = x^m/n
                          So,     = 4^5/5 * 27^2/2
                                  = 4¹ * 27¹
                                              = 4 * 27
                                              = 108
        Answer:   108
Examples for radical with exponent math problem 2:
              Simplify the math radical `(root4 5)^3 * (sqrt5)^3`
        Solution:
                     Given radicals `(root4 5)^3 * (sqrt5)^3`
                                              = `(root4 5)^3 * (sqrt5)^3`
              we know the math radical rule with an exponents  ( `root(n)(x)` )^m = x^m/n
                          So,     = 5^3/4 * 5^3/2
                                  = `5` ^{(`3/4` + `3/2` )}
                                              = 5^9/4
             Answer:  5^9/4