化根号内（a的2n加3次方×b的2m加1次方）为最简二次根式（m、n为正整数,a＞0,b＞0）过程怎么写?

题目

化根号内（a的2n加3次方×b的2m加1次方）为最简二次根式（m、n为正整数,a＞0,b＞0）过程怎么写?

答案

√[a^(2n+3)*b^(2m+1)]
=√[a^(2n+2+1)*b^(2m+1)]
=√[a*a^(2n+2)*b*b^(2m)]
=√{a*[a^(n+1)]^2*b*(b^m)^2}
=a^(n+1)*b^m*√ab