Are the square roots of all positive integers irrational?

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Kuldeep Guha Mazumder

Mathematics tutor with 6 years of experience

sqrt (4)=+/-2 is not an irrational. Remember one thing, sqrt(4) or (4)^(1/2) refers to the roots of the equation x^2=4 and fundamental theorem of algebra asserts that there are two such complex roots (real complex in this case, viz., 2 and -2). But whenever you use the radical sign you are actually referring...
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sqrt (4)=+/-2 is not an irrational. Remember one thing, sqrt(4) or (4)^(1/2) refers to the roots of the equation x^2=4 and fundamental theorem of algebra asserts that there are two such complex roots (real complex in this case, viz., 2 and -2). But whenever you use the radical sign you are actually referring to the non-negative square root (or more generally if we speak in the complex domain, the principal square root) that is only 2 in this case. read less
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Qualified (Engg from NIT) & experienced mentor with 6+ yrs experience.

No. All square roots of integers are not irrational. Examples: SQRT(1) = plus/minus 1, SQRT (4) = plus/minus 2....This way sqrt root of 9, 16, 25...............are rational.
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Not Necessary
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No. Not all square roots of integers are irrational. Examples are 1
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No.
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Qualified (Engg from NIT) & experienced mentor with 6+ yrs experience.

No, Examples are 1,4,9 whose sq root are not irrational
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