Show an example of a rational number that is between √10 and √11
One example of a rational number between √10 and √11 is 3.162.
To find a rational number between √10 and √11, we can rationalize the denominators of these square roots.
Step 1: Rationalize √10:
√10 = √(10 * 1) = √(2 * 5 * 1) = √(2 * 5) = √2 * √5 = √2√5
Step 2: Rationalize √11:
√11 = √(11 * 1) = √(11 * 1) = √(11 * 1) = √11
So, a rational number between √10 and √11 is:
(√2√5 + √11) / 2
Simplifying this expression further will give you the exact rational number between √10 and √11.