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

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`sqrt(343x ^13)`

`=sqrt(7^3*x^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:

`sqrt(7^2*7*x^2*x^2*x^2*x^2*x^2*x^2*x)`

`=7*x^6sqrt(7*x)`

`=7x^6sqrt(7x)`

**This is the required answer.**

**Sources:**

`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(7x)^(1/2)`

`=7x^6 sqrt(7x)`

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)`

`=7x^6sqrt(7x)`

`you can`

`apply`

`(x^m)^n=x^(mn)` rule.