Answer:
t
Step-by-step explanation:
[tex]\sqrt{\frac{(t^{2}+t)(t^{3}+t^{2})}{(t^{2}+t)+(t^{3}+t^{2})}}[/tex]
looking at the denominator we are going to factor out like terms
[tex]{(t^{2}+t) commonterm "t" +(t^{3}+t^{2})commonterm "t^{2} }}"[/tex]
t ( t + 1) + [tex]t^{2}[/tex] ( t + 1) combine like terms (t+1) similar: 3x + 2x
add coefficients time like term. (3+2)x or 5x
(t+[tex]t^{2}\\[/tex]) (t+1) new denominator
[tex]\sqrt{\frac{(t^{2}+t)(t^{3}+t^{2})}{(t+t^{2})(t+1) }}[/tex] replaced with new denomimator. cancel [tex]\frac{t^{2}+t }{t+t^{2} }[/tex]
[tex]\sqrt{\frac{(t^{3}+t^{2})}{(t+1) }}[/tex] factor out GCF numerator
[tex]\sqrt{\frac{t^{2} (t+1)}{(t+1) }}[/tex] cancel (t+1)/(t+1)
[tex]\sqrt{t^{2} }[/tex] = t
