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

$\sqrt[4]{x^{40}}=x^{10}$