Question 182354
I'll do the first one to get you started.


# 1


{{{sqrt(5)*(2*sqrt(45)-sqrt(5))}}} Start with the given expression



{{{sqrt(5)*(2*3*sqrt(5)-sqrt(5))}}} Simplify {{{sqrt(45)}}} to get {{{sqrt(45)=sqrt(9*5)=sqrt(9)*sqrt(5)=3*sqrt(5)}}}



{{{sqrt(5)*(6*sqrt(5)-sqrt(5))}}} Multiply



{{{sqrt(5)*(5*sqrt(5))}}} Combine like terms. Note: {{{6*sqrt(5)-sqrt(5)=(6-1)*sqrt(5)=5*sqrt(5)}}}



{{{5*sqrt(5)*sqrt(5)}}} Rearrange the terms.



{{{5*sqrt(5*5)}}} Combine the roots.



{{{5*sqrt(25)}}} Multiply



{{{5*5}}} Take the square root of 25 to get 5



{{{25}}} Multiply



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Answer:


So {{{sqrt(5)*(2*sqrt(45)-sqrt(5))=25}}}