Question

2 = 141
Estimation
Square root of a number can also be estimated by finding the number whose square is the closest to
the given mumber. In this method we start from a broad range and then start narrowing the
range
we find the answer
We can also estimate the number of digits in the square root of number.
It can be understood by the following example
Example 26: Estimate the square root of 500.
Solution: As we know that, 500 is greater than 400 but less than 900
Thus 400 < 500 < 900
Hence, 400 < 1500 < 900
Since 400 = 20 and 900 = 30 so, 20 < 500 < 30.
Now, narrow the range of estimation,
Between 20 and 30, we know that, (22) = 484 and (23) = 529.
Thus 22 < 500 < 23.
Here 500 is closer to 484 than 529.
Thus, V500 is approximately equal to 22.
Example 27: Estimate the value of 250.
Solution: As we know that, 250 is greater than 100 but less than 400.
Thus 100 < 250 < 400
Hence, 100 < V250 <1400
61​

Answer 1

Answer:

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Answer 2

Answer:

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