Irrational Numbers

Prove that $\sqrt{2}$ is an irrational number

Division of two irrational numbers is:

The difference of two irrational numbers is also an irrational number.

Compare $3$ and $\sqrt{5}$

Compare $2$ and $\sqrt{5}$

Compare $\sqrt{2}$ and $\sqrt{5}$

Compare $\sqrt{2}$ and $\sqrt{3}$

The product of a rational number and an irrational number is irrational number.

Prove that $7-2\sqrt{11}$ is irrational.

Prove that $7+2\sqrt{11}$ is irrational.

Prove that $\sqrt{2}-\sqrt{11}$ is irrational.

Prove that $\sqrt{2}+\sqrt{11}$ is irrational.

Prove that $5\sqrt{17}$ is an irrational number.

Prove that $2-\sqrt{2}$ is an irrational, if $\sqrt{2}$ is an irrational number.

Divide $45\sqrt{7}$ by $5\sqrt{7}$.

Divide $12\sqrt{5}$ by $2\sqrt{5}$.

Evaluate: $\frac{7}{2}-\frac{4\sqrt{2}}{11}$

Evaluate: $\frac{\sqrt{3}}{2}-\frac{2}{5}$

Find the sum of $\sqrt{5}$ and $\frac{4}{5}$.

Find the sum of $3\sqrt{2}$ and $\frac{3}{5}$.