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# question

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

Sep 12, 2017

#1
+2337
+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.
Sep 13, 2017
#2
+7348
+2

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

hectictar  Sep 13, 2017
#3
+2337
+1

Clever indeed!

TheXSquaredFactor  Sep 15, 2017