The recurring decimal 0.444… (the digit 4 repeating) is exactly 4/9. What is its square root?

Take the root of the top and the bottom separately: √(4/9) = √4 ÷ √9 = 2/3, and 2/3 written as a decimal is 0.666… . The check is quick: 0.666… × 0.666… = $(2/3{)}^2=4/9=0.444$… ✓. The trap 0.222… halves the decimal instead of taking its root — halving is what gives 0.222…, since 4/9 ÷ 2 = 2/9. The terminating 0.66 looks close but is not equal, as $0.66^2=0.4356$ rather than 0.4444…, and 0.2 is the square root of 0.04.