Question

Simplify Nth Root Radicals (Type 1)May 20,1:34:01 PMWatch help videoGiven x > 0, simplify V x40 completely.

Answer 1

Given

`x>0`

Let's factorize the expression appropriately.

`\sqrt[4]{x^4\cdot x^4\cdot x^4\cdot x^4\cdot x^4\cdot x^4\cdot x^4\cdot x^4\cdot x^4\cdot x^4}=\sqrt[4]{x^(40)\text{ }}^{}`

Now, every time we see an

`x^4`

inside the root, we can take it outside the root as an x. So we'll have

`\sqrt[4]{x^4\cdot x^4\cdot x^4\cdot x^4\cdot x^4\cdot x^4\cdot x^4\cdot x^4\cdot x^4\cdot x^4}=x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x=x^(10)`

In conclussion

`\sqrt[4]{x^(40)}=x^(10)`