How would you simplify the square root of 125 times(x) the cube root of 25?

Question

How would you simplify the square root of 125 times(x) the cube root of 25?

Answer 1

first of all....

125 = 5^3, 25= 5^2

So,125^(1/2) = 5^(3/2) , 25^(1/3) = 5^(2/3)

then,125^(1/2) x 25^(1/3) = 5^(3/2) x 5^(2/3) = 5^( 3/2 + 2/3) = 5^(13/6)

Answer 2

preparation: 125 = 5^3, 25= 5^2

So,125^(1/2) = 5^(3/2) , 25^(1/3) = 5^(2/3)

then,125^(1/2) x 25^(1/3) = 5^(3/2) x 5^(2/3) = 5^( 3/2 + 2/3) = 5^(13/6)

The answer:  5^(13/6)