MediumMathematicsHigh School (9–10)GeneralNumber Systems › Rational and Irrational NumbersNumericalBoard Exam
A square garden has an area of 18 m². Find its side, its perimeter and its diagonal…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A square garden has an area of . Find its side, its perimeter and its diagonal. Which of the three lengths are irrational? Give the perimeter to two decimal places.
Need a reminder? The key ideaShow
Rational plus irrational is irrational. A non-zero rational times an irrational number is irrational. Two irrational numbers can give a rational or an irrational sum or product. To prove that a number is irrational, suppose it is rational and get a known irrational root alone.
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 side. . A non-zero rational times : irrational.
Step 2. The perimeter. to two places. Also irrational.
Step 3. The diagonal. . Two irrational factors give a rational length.
Answer: side and perimeter are irrational; the diagonal, , is rational.
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