write the expression in lowest terms. assume that all variables represent positive real numbers.

Question

A). (12)-(24)(√14)/(16)              B). (10x)-(√250x^3)/(2x)

Answer 1

A)  12 - (24√(14))/16

      Note that the prime factorization of 14 is 7(2) so there are no perfect squares to remove from

     underneath the square root sign.

     We can divide out 8 from both 24 and 16 to reduce the fraction so we have:

 

     12 - (24√(14))/16 = 12 - (3√(14))/2

 

B)  10x - √(250x³)/(2x)

     We can factor out the 250x³ within the square root sign to (25)(10)(x²)(x)

     which is (5²)(10)(x²)(x)

     The reason we do this is that any squared terms under the √ sign can be brought out

     from under the square root...  Note:  √x² = x so...

 

    10x - √(250x³)/(2x) = 10x - ((5x)√(10x))/(2x)

    In the fraction the numerator and denominator both have the term 'x' so we can

    eliminate the x by dividing it out since x/x = 1   so

 

    10x - ((5x)√(10x))/(2x) = 10x - (5√(10x))/2