Question 248009


{{{sqrt(245*k^7*q^8)}}} Start with the given expression.



{{{sqrt(49*5*k^7*q^8)}}} Factor {{{245}}} into {{{49*5}}}



{{{sqrt(49*5*k^2*k^2*k^2*k*q^8)}}} Factor {{{k^7}}} into {{{k^2*k^2*k^2*k}}}



{{{sqrt(49*5*k^2*k^2*k^2*k*q^2*q^2*q^2*q^2)}}} Factor {{{q^8}}} into {{{q^2*q^2*q^2*q^2}}}



{{{sqrt(49)*sqrt(5)*sqrt(k^2)*sqrt(k^2)*sqrt(k^2)*sqrt(k)*sqrt(q^2)*sqrt(q^2)*sqrt(q^2)*sqrt(q^2)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{7*sqrt(5)*sqrt(k^2)*sqrt(k^2)*sqrt(k^2)*sqrt(k)*sqrt(q^2)*sqrt(q^2)*sqrt(q^2)*sqrt(q^2)}}} Take the square root of {{{49}}} to get {{{7}}}.



{{{7*sqrt(5)*k*k*k*sqrt(k)*sqrt(q^2)*sqrt(q^2)*sqrt(q^2)*sqrt(q^2)}}} Take the square root of {{{k^2}}} to get {{{k}}}.



{{{7*sqrt(5)*k*k*k*sqrt(k)*q*q*q*q}}} Take the square root of {{{q^2}}} to get {{{q}}}.



{{{7k^3q^4*sqrt(5k)}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(245*k^7*q^8)}}} simplifies to {{{7k^3q^4*sqrt(5k)}}}



In other words, {{{sqrt(245*k^7*q^8)=7k^3q^4*sqrt(5k)}}} where every variable is non-negative.