Question 325222
{{{sqrt(1575*x^4)}}} Start with the given expression.



{{{sqrt(225*7*x^4)}}} Factor {{{1575}}} into {{{225*7}}}



{{{sqrt(225*7*x^2*x^2)}}} Factor {{{x^4}}} into {{{x^2*x^2}}}



{{{sqrt(225)*sqrt(7)*sqrt(x^2)*sqrt(x^2)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{15*sqrt(7)*sqrt(x^2)*sqrt(x^2)}}} Take the square root of {{{225}}} to get {{{15}}}.



{{{15*sqrt(7)*x*x}}} Take the square root of {{{x^2}}} to get {{{x}}}.



{{{15x^2*sqrt(7)}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(1575*x^4)}}} simplifies to {{{15x^2*sqrt(7)}}}



In other words, {{{sqrt(1575*x^4)=15x^2*sqrt(7)}}} where {{{x>=0}}}