Question 399361
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Hi
1: {{{sqrt(48a^5b)/ sqrt(12ab) = sqrt(16*3a^5b)/ sqrt(4*3ab)= 4*sqrt(3a^5b)/ (2*sqrt(3ab)) = 2*sqrt(3a^5b)/(sqrt(3ab)) = 2*sqrt(a^4)  }}}

2: sqrt5(2sqrt45 - sqrt5)= 2sqrt(225) - 5 = 30 - 5 = 25
3: 7 /(1- sqrt3) = 7*(1+sqrt(3) )/((1- sqrt3)(1+sqrt(3)) = (-7/2)(1+sqrt(3))
Rules of Exponents:
I.  {{{x^m*x^n = x^(m+n) }}}   
II.  {{{(a^p)^q = a^(p*q)}}}
III. {{{root(a,p)*root(a,q) = root(a,p*q)}}}