Which irrational number is between /14 and /18

One possible irrational number between 1/4 and 1/8 is π/6 (pi/6).

To find an irrational number between 1/4 and 1/8, we can use the fact that there are infinitely many irrational numbers between any two rational numbers.

One such irrational number is √2/4.

To confirm that √2/4 is irrational and lies between 1/4 and 1/8, we can simplify it and compare it to the given range.

√2/4 simplifies to approximately 0.35355.

1/4 is equal to 0.25, while 1/8 is equal to 0.125.

Therefore, √2/4 falls between 1/4 and 1/8, and is an irrational number.

To find an irrational number between two fractions, we need to convert those fractions into decimal form and then find an irrational number between their decimal equivalents.

Let's start by calculating the decimal equivalents of the fractions /14 and /18.

To convert a fraction to a decimal, divide the numerator by the denominator:

/14 = 0.07142857 (approx.)

/18 = 0.05555556 (approx.)

Now, we can try to find an irrational number between these two decimal values.

Since irrational numbers cannot be expressed as fractions or decimals that terminate or repeat, one approach is to find a well-known irrational number that falls within that range.

One well-known irrational number is π (pi), which is approximately equal to 3.14159265358979323846.

Checking the value of π, we can see that it is greater than 0.07142857 (/14) and smaller than or equal to 0.05555556 (/18). So, in this case, π does not fall within the desired range.

We need to continue searching for another irrational number.

Another well-known irrational number is √2 (square root of 2), which is approximately equal to 1.41421356.

Checking the value of √2, we can see that it is smaller than 0.07142857 (/14) and greater than or equal to 0.05555556 (/18). Thus, √2 falls within the desired range (/14, /18).

Therefore, √2 is an irrational number between /14 and /18.