Question 184960
{{{sqrt(45)+sqrt(80)}}} Start with the given expression



{{{sqrt(9*5)+sqrt(16*5)}}} Factor 45 into 9*5 and factor 80 into 16*5. Note: each factorization has a perfect square factor.



{{{sqrt(9)*sqrt(5)+sqrt(16)*sqrt(5)}}} Break up the square root.



{{{3*sqrt(5)+4*sqrt(5)}}} Take the square root of 9 to get 3. Take the square root of 16 to get 4



{{{(3+4)*sqrt(5)}}} Factor out the GCF {{{sqrt(5)}}}



{{{7*sqrt(5)}}} Combine like terms



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Answer:


So {{{sqrt(45)+sqrt(80)=7*sqrt(5)}}}