Question

What is the simplified form of the radical expression: V1000. Show all steps when factoring. Show that the sum of two irrational numbers can be rational or irrational. Provide two exampl

Answer 1

1) The simplified form of this radical expression:

`\sqrt[]{1000}=\sqrt[]{10^2*10}\text{ =10}\sqrt[]{10}`

2) The sum of two irrational numbers is irrational

Example:

√2 + √2 = 2√2

2√2≈2.828427125....

π+π = 2π = 6.283185307...

Since these two sums can't be written as a fraction (ratio) then they are irrational (a/b). Notice that these numbers are infinite and nonperiodic.