Q:

How do you calculate square roots?

A:

Quick Answer

Calculating square roots can either be done by hand or with a calculator. With a calculator, calculating a square root is as easy as pressing the number followed by the square root sign. These numbers are often long and are in decimal form.

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Full Answer

To calculate the square root of a number by hand, one can use a variety of approaches. If the goal is to simplify the square root, you could, for example, change the square root of 50 into 5 times the square root of 2. Reducing the number to its simplest terms is always a good solution to finding the square root of a number.

Going further, by hand, involves estimation first. In the previous example, 5 times the square root of 2 can be estimated by multiplying 5 by 1.41, which is the square root of 2, to get approximately 7.1. For a larger number, you could find the square root using prime factorization.

For example, to find the square root of 2,000, you could find the square roots of 500 and 4, which are multiplied together to equal 2,000. The square root of 4 is 2, and the square root of 500 is 5 times the square root of 20, which is 10 times the square root of 5. Overall, the square root of 2,000 is then 20 times the square root of 5, or approximately 40.

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