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mymachine
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Is there any method to find the exact value of the square root of 3,5,7,11,13,14,15,17,18, etc.?
Thank you
Thank you
lavinia said:If instead of a infinite decimal expansion you would accept some other infinite expression then you can express the square root of 2 as an infinite continued fraction.
The exact value of the square root of 3 is approximately 1.7320508075688772.
The square root of 5 can be calculated by using a calculator or by using the long division method to find the decimal approximation. The exact value of the square root of 5 is approximately 2.23606797749979.
Unfortunately, there is no simple way to find the exact value of the square root of 7. It is an irrational number and cannot be expressed as a finite decimal or fraction. The decimal approximation for the square root of 7 is approximately 2.6457513110645907.
No, it is not possible to find the exact value of the square root of 11 without using a calculator. Similar to square root of 7, it is also an irrational number and cannot be expressed as a finite decimal or fraction.
You can check if your answer for the square root of a number is correct by squaring it. For example, if you have calculated that the square root of 7 is approximately 2.6457513110645907, you can check it by squaring 2.6457513110645907 which should give you a result close to 7. It may not be exactly 7 due to rounding errors, but it should be close enough.