Question

Add. Simplify by collecting like radical terms if possible, assuming that all expressions under radicals represent nonnegative numbers.

sqrt10a +2sqrt90a^3

I'm confused. How do I go about solving this?

Answer 1

the square roots go all the way across the problem

Answer 2

is the answer 10?

Answer 3

First, we can simplify \[\sqrt{90a^3}\] like so


\[\sqrt{90a^3}\]


\[\sqrt{9*10a^2*a}\]


\[\sqrt{9}*\sqrt{10}*\sqrt{a^2}*\sqrt{a}\]


\[3*\sqrt{10}*a*\sqrt{a}\]


\[3a*\sqrt{10a}\]


So \[\sqrt{90a^3}=3a*\sqrt{10a}\]


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Now this means that the original expression \[\sqrt{10a}+2\sqrt{90a^3}\] turns into this \[\sqrt{10a}+2*3a*\sqrt{10a}\]


\[\sqrt{10a}+2*3a*\sqrt{10a}\]


\[\sqrt{10a}+6a\sqrt{10a}\]


\[(1+6a)\sqrt{10a}\]



So in the end, \[\sqrt{10a}+2\sqrt{90a^3}=(1+6a)\sqrt{10a}\]