What 3-digit number is a perfect square and a perfect cube? Algebra Radicals and Geometry Connections Simplification of Radical Expressions 1 Answer George C. Jun 28, 2015 #729=9^3=27^2# Explanation: The answer must be #a^6# for some integer #a# due to the properties of exponentiation. Only #3^6 = 729# lies in the required range. #3^6 = (3^2)^3 = 9^3# #3^6 = (3^3)^2 = 27^2# Answer link Related questions How do you simplify radical expressions? How do you simplify radical expressions with fractions? How do you simplify radical expressions with variables? What are radical expressions? How do you simplify #root{3}{-125}#? How do you write # ""^4sqrt(zw)# as a rational exponent? How do you simplify # ""^5sqrt(96)# How do you write # ""^9sqrt(y^3)# as a rational exponent? How do you simplify #sqrt(75a^12b^3c^5)#? How do you simplify #sqrt(50)-sqrt(2)#? See all questions in Simplification of Radical Expressions Impact of this question 9466 views around the world You can reuse this answer Creative Commons License