MediumMathematicsHigh School (9–10)GeneralNumber Systems › Rational and Irrational NumbersNumericalBoard Exam
Between which two whole numbers next to each other does √110 lie? …
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Between which two whole numbers next to each other does lie? Is it nearer to the smaller one or to the larger one? Check with its value to two decimal places.
Need a reminder? The key ideaShow
Every real number is a point on the number line. Between any two numbers there are infinitely many rational numbers, such as their average. The square root spiral builds , , and so on, one triangle at a time.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The squares. and , so .
Step 2. Which is nearer? is above and below , so the root is a little nearer to .
Step 3. Check. , just below the middle, .
Answer: between and , a little nearer to .
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