Question

What is the square root of x^19??
I have such a hard time understanding how to do these... final tomorrow morning!

Answer 1

two goes in to 19 9 times with a remainder of one
so \(x^9\) comes outside the radical and \(x^1=x\) stays inside the radical

Answer 2

i.e.
\[\sqrt{x^{19}}=x^9\sqrt{x}\]

Answer 3

this simple method always works
for example
\[\sqrt{x^{11}}=x^5\sqrt{x}\] and
\[\sqrt[3]{x^{17}}=x^5\sqrt[3]{x^2}\]

Answer 4

I don't know what I'd do without you, @satellite73 :) Ok, so what if I have something like; the square root of 175x^10

Answer 5

in this case \(\sqrt{x^{10}}=x^5\) since 2 goes in to 10 5 times with no remainder

Answer 6

as for \(\sqrt{175}\) you have to know that \(175=25\times 7\) and so \[\sqrt{175}=\sqrt{25\times 7}=\sqrt{25}\sqrt{7}=5\sqrt{7}\]

Answer 7

therefore
\[\sqrt{175x^{10}}=5x^5\sqrt{7}\]

Answer 8

So is my original question's answer: x^9 and square root of x