Radicals. Simplify the expression. Give the exact value in simplified form. Rationalize any demoninators. the square root of 343x ^13

Expert Answers
rakesh05 eNotes educator| Certified Educator

`sqrt(343x^13)` =`sqrt(7^3 x^13)`

                 `=(7^2 7.x^12 x)^(1/2)`      

(by law of the exponent  `(x^m)^n=x^(mn)` .)


                 `=7x^6 sqrt(7x)`


llltkl | Student

`sqrt(343x ^13)`


To simplify a square root, "take out" anything that is a "perfect square" that is, you take out front anything that has two copies of the same factor:




This is the required answer.

aruv | Student

question is

`sqrt(343x^13)=sqrt(7xx7xx7xx x^13)`

`=(7^3xx x^13)^(1/2)`

`=(7^3)^(1/2)xx (x^13)^(1/2)`

`=7(7)^(1/2)xx x^6 (x)^(1/2)`


`you can`


`(x^m)^n=x^(mn)`  rule.