Describe how you would estimate the square root of a number that is not a perfect square without using a calculator.
2 answers:
The square root must be between the square roots of the perfect squares just above and just below your number.
<span>For example the square root of 89 must be between 9 and 10.</span>
Answer:
We will take a number say 105. To find its square root, proceed as under:
- Find the closest perfect square to it. Here, it is 100.
- Find square root of that number, i.e. 100. We know the square root is 10.
- Divide the number by the square root calculated above. Here, 105÷10.
- Take the mean of the result obtained above and the square root in step 2. Here, (10+10.5)/2 = 10.25
The number obtained above is the square root of the required number.
Also we can consider second example as:
We have to find square root of 420.
-
Closest perfect square is 400.
- Square root of 400 is 20.
- Mean of 20 and 21 is 20.5
- Square root of 420 is 20.5
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Step-by-step explanation:
