AP TET Paper 2 Math and Science Model Paper 3

Concept:A number is irrational if it cannot be expressed as $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$.Explanation:We know $1000000 = 10^6$.So the given roots can be written as powers of $10$.$\sqrt[6]{1000000} = \sqrt[6]{10^6} = 10^{6/6} = 10^1 = 10$, which is rational.$\sqrt{1000000} = \sqrt{10^6} = 10^{6/2} = 10^3 = 1000$, which is rational.$\sqrt[3]{1000000} = \sqrt[3]{10^6} = 10^{6/3} = 10^2 = 100$, which is rational.$\sqrt[4]{1000000} = \sqrt[4]{10^6} = 10^{6/4} = 10^{3/2} = \sqrt{10^3} = \sqrt{1000} = 10\sqrt{10}$.Since $\sqrt{10}$ is a non-terminating, non-recurring decimal, $10\sqrt{10}$ is irrational.Therefore, the irrational number among the given options is $\sqrt[4]{1000000}$.Answer:Option C $\sqrt[4]{1000000}$