How do you simplify #4 sqrt (81/16)#?

1 Answer
Aug 7, 2016

Answer:

#3/2#

Explanation:

If you recognise 81 and 16 as being 4th powers, the answer is easy to write down as #3/2#

Otherwise write each number as the product of its prime factors:

#root4(81/16) = root4((3xx3xx3xx3)/(2xx2xx2xx2))=root4((3^4)/(2^4)) = 3/2#

The 4th root is easy to find if you remember it is the square root of a square root.

81 and 16 are both perfect squares, but their square roots are also squares.

#root4(81/16) = sqrt(sqrt(81/16) ) = sqrt(9/4) = 3/2#