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?
问题描述:
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
√[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