State where \left( {\sqrt 6  + \sqrt 9 } \right) is rational or not.

Foundation

Mathematics Foundation

Properties of Real Number

Irrational Number

Linear Equations in One Variable

Question

State where

\left( {\sqrt 6&nbsp; + \sqrt 9 } \right)

is rational or not.

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Given number is

\sqrt{6} + \sqrt{9}

\sqrt{9} = 3

Hence, the number is

\sqrt{6} + 3

We know that

\sqrt{6}

is an irrational number while

3

is a rational number.

We also know that, the sum of a rational number and an irrational number is always an irrational number.

Hence,

\sqrt{6} + \sqrt{9}

is an irrational number.