Question

Find the exact value of the radical expression in simplest form.
the square root of s to the eighth power + the square root of 25 times s to the eighth power + 2 the square root of s to the eighth power − the square root of s to the fourth power

8s4

28 times s to the fourth power times the square root of s

8s4 − s2

28 times s to the fourth power times the square root of s − s2

Answer 1

\[\sqrt{s ^{8}} + \sqrt{25s ^{8}} + 2\sqrt{s ^{8}} - \sqrt{s ^{4}}\]

Answer 2

\[\large \sqrt{s ^{8}} + \sqrt{25s ^{8}} + 2\sqrt{s ^{8}} - \sqrt{s ^{4}}\]You can rewrite this equation. You should already know that a square root, \(\sqrt{x}\) can be rewritten as \(x^{1/2}\)

Taking that property, lets write all our terms to the half power. This will make it easier for us to evaluate.

Answer 3

\begin{align}
\large \sqrt{s ^{8}} + \sqrt{25s ^{8}} + 2\sqrt{s ^{8}} - \sqrt{s ^{4}} &= \large s^{8/2} +(25^{1/2})(s^{8/2}) +2(s^{8/2})-s^{4/2} \\
&= \large s^4 +(5)(s^4)+2(s^4)-s^2 \\
&=\large s^4 +5s^4 +2s^4 -s^2 \\
&=\large 6s^4 +2s^4 -s^2 \\
\end{align}

Answer 4

Thank you (: But that answer isnt in my multiple choice answers?

Answer 5

What do you get when you simplify this?

Answer 6

8s^4 -s^2

Answer 7

There you go :)

Answer 8

Yay! Thanks! Can you help with more?

Answer 9

I can try.