Question

Is the square root of 3 a rational number

Answer 1

No.

Explanation:

The square root of 3 is an irrational number. 3 is not a perfect square (such as 9 or 25 or 100) The square root of a perfect square is rational. for example:

`√(25) = 5` or
`√(49) = 7` or
`\sqrt{(81)/(4) } = (9)/(2)`

All the square roots of all the numbers that aren't perfect squares,

`√(2) , √(3) , √(5) , √(6) , √(7) , √(8) , √(10)` etc are all irrational numbers.

Answer 2

Explanation:

No - a rational number can be written as a fraction like 1/2, 2/5, 7/1.

√3 is not rational . It is classed as irrational.

If we use a manual method to find out we find that its a decimal number which carries on without bounds.

Using a scientific calculator we get the value 1.732050808 but the decimals numbers go on and on - the calculator has limited memory so can only give a value to 9 places.

All values like √2, √5, √17 ( where the square root is not an integer) are irrational.