What is the square root of the square root of the square root of 5?

Question

No calculator allowed. Please explain process if possible.

Answer 1

sqrt(sqrt(sqrt(5))) = (((5^0.5)^0.5)^0.5 = 5^(0.5^3) = 5^0.125 = 1.222844545

There is no way to compute the square root of the square root of the square root of 5 without using a calculator. The only thing you can do is simplify the expression. You can write it as 5^0.125, 5^(1/8), or the eighth root of 5 (written just like sqrt(8), but with a little number 8 sitting in the v-shaped part of the radical sign), because the rules of exponents say that you can multiply exponents when one exponential expression is raised to some power.

Answer 2

square root of the square root of the square root of 5 =
((((5^1/2))^1/2)^1/2)=5^(1/8)

Answer 3

x = 5^8

Answer 4

just use a calculator, jeez