I got no clue

[dollyayesha2345]

Question: Find a real number between 1 and$\sqrt3$

My approach(which is wrong): $\frac{a+b}{2}$
$$\frac{1+1.732}{2}$$$$=\frac{2.732}{2}$$$$=1.366$$So a real number between 1 and$\sqrt3$ is 1.3.

Please tell me whether my approach and answer is correct or not. If not then do guide me on how to solve this.

 

[Harry_the_cat]

Your approach looks fine to me. Maybe you should indicate that sqrt(3) is approximately equal to 1.732.

1.3 is a real number between 1 and sqrt(3). Your answer is correct.

 

[Dr.Peterson]

Question: Find a real number between 1 and$\sqrt3$

My approach(which is wrong): $\frac{a+b}{2}$
$$\frac{1+1.732}{2}$$$$=\frac{2.732}{2}$$$$=1.366$$So a real number between 1 and$\sqrt3$ is 1.3.

Please tell me whether my approach and answer is correct or not. If not then do guide me on how to solve this.

I agree that your answer is correct, and the method is good; it's probably good to add that there are very many (infinitely many!) other correct answers, such as (picking two randomly) 1.71629, and 5/3 = 1.666... .

What's good about your method is that it is guaranteed to produce a number between the two given numbers, whatever they were. So your answer is better in some sense than mine!

 

[dollyayesha2345]

@Harry_the_cat @Dr.Peterson thank you so much!

 

[Dr.Peterson]

I just noticed one more thing I should have said.

The method I said could be considered "better" than mine in a sense would stop at $\frac{1+\sqrt{3}}{2}\approx 1.366$. When you rounded that down to 1.3, you were actually doing the same thing I did, looking at the digits of a value and choosing a number between 1 and that number! Your final answer is a rational number in the interval; your method found an irrational number, which is a very nice answer to the question.