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what is the answer to the square root of 108b to the 4th power

Guest Sep 12, 2017
 #1
avatar+2268 
+2

Your question appears to want one to evaluate the expression \(\sqrt{(108b)^4}\). Let me try to make it easier so that the calculator is not necessary:

 

\(\sqrt{(108b)^4}\) Of course, the square root can also be represented as the power to 1/2.
\(\left((108b)^4\right)^\frac{1}{2}\) Using the power rule, we know that \(\left(a^b\right)^c=a^{b*c}\). Let's apply that.
\(\left((108b)^4\right)^\frac{1}{2}=(108b)^{4*\frac{1}{2}}=(108b)^2\) Now, distribute the exponent.
\((108b)^2=108^2*b^2\) Now, let's simplify 108^2 by doing this.
\(108^2=(100+8)(100+8)=10000+800+800+64=11664\) This, to me, is the easiest way to calculate the square of a number without a calculator. What do you think?
\(11664b^2\) This is your final answer.
   
TheXSquaredFactor  Sep 13, 2017
 #2
avatar+7336 
+2

I think that's a really clever way to get the square of 108 !  laugh

hectictar  Sep 13, 2017
 #3
avatar+2268 
+1

Clever indeed!

TheXSquaredFactor  Sep 15, 2017

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