 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that evaluate using positive square root minus 11 whole square into square root of 144 whole upon cube root of minus 64. Before starting the solution of this question, we should know some results and these are square of a negative number is positive. Two square roots of any positive number say n are given by square root of n and minus square root of n where square root of n will be the positive square root of n and minus square root of n will be called as negative square root of n and cube root of a positive number is positive and cube root of a negative number is negative. With this key idea we shall move on to the solution. We have to evaluate the expression minus 11 whole square into square root of 144 whole upon cube root of minus 64. Let us first simplify this expression. In numerator we have minus 11 whole square that is equal to minus 11 into minus 11 and that is equal to 121. From the key idea we know that square of a negative number is positive and here also we have got the square of this negative number as positive. Now we shall also evaluate square root of 144. We know that 12 square is equal to 144 and minus 12 whole square is equal to 144 thus square root of 144 will be equal to 12 and minus 12 where 12 is positive square root and minus 12 will be negative square root that is we are using the second result given in the key idea where two square roots of any positive number say n are given by positive square root of n and negative square root of n but in the question we are given to use positive square root thus we take square root of 144 is equal to 12 now we are given cube root of minus 64 in denominator and from the key idea we know that cube root of a positive number is positive and cube root of a negative number is negative now we know that minus 4 whole cube is equal to minus 64 thus cube root of minus 64 will be equal to minus 4 as cube root of a negative number is negative so now we have minus 11 whole square is equal to 121 square root of 144 is equal to 12 and cube root of minus 64 is equal to minus 4 now we put all these simplified terms in the given expression and we get minus 11 whole square into square root of 144 whole upon cube root of minus 64 and this is equal to 121 into 12 whole upon minus 4 on solving further we get 121 into 3 whole upon minus 1 that is equal to minus 363 thus the given expression is equal to minus 363 this is the required answer this completes our session hope you enjoyed this session