Is is square root of 1.6875 a rational number

Question:

Is square root of 1.6875 a rational number ?

Square root of 1.6875 a rational number is not a rational number

Solution:

Given that we have to find square root of 1.6875 and determine if it is rational number or not

Let us first find square root of 1.6875

Let us understand about rational number

A rational number is a number that can be expressed as a fraction (ratio) in the form where p and q are integers and q is not zero.

When a rational number fraction is divided to form a decimal value,  it becomes a terminating or repeating decimal.

So the number 1.29903810568 is not a rational number

In other words we can say,

Only the square roots of square numbers are rational. Here 1.6875 is not a perfect square. So it is not rational number

1/800 is the right answer