Often i have encountered the phrases $x$ square and $x$ squared for $x^2$.

My question is: Are both the phrases correct or is any one of them incorrect. If both of them are correct, is there any difference between their meaning and their usage or are both the same is meaning and have the same usage?

  • $\begingroup$ In most contexts. "x square" is fine, and "x squared", while comprehensible, sounds a little weird. $\endgroup$ – quasi Mar 21 '17 at 3:46
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    $\begingroup$ I have never heard the phrase "x square" in any context, much less to represent $x^2$. The phrase "x squared" although not following usual rules of grammar, is in common use in the English language to refer to the variable $x$ being raised to the power of two., a sort of shortened form of the phrase "the variable x (which has been) squared" which is following proper grammar rules $\endgroup$ – JMoravitz Mar 21 '17 at 3:46
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    $\begingroup$ A google search for the phrase "x square" in quotes returns only 496k results, and none of the top results seem to be in reference to $x^2$, meanwhile a search for the phrase "x squared" in quotes returns 4.5mil, all of the top results in reference to $x^2$. $\endgroup$ – JMoravitz Mar 21 '17 at 3:49
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    $\begingroup$ @JMoravitz that's as close to an answer as anybody is going to get $\endgroup$ – c.. Mar 21 '17 at 3:57
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    $\begingroup$ @quasi I've always heard the pythagoarean theorem as "a squared plus b squared = c squared". I've usually heard numbers squared but for physical distances I've heard 100 meters square if the speaker is british and 100 meters squared if the speaker is american. They are interchangeable. I very much prefer "squared" but I'm only speaking for myself. $\endgroup$ – fleablood Mar 21 '17 at 4:29

The expression $b^2 = b ⋅ b$ is called "the square of b".

It is pronounced "b squared".

The expression $b^3 = b ⋅ b ⋅ b$ is called "the cube of b".

It is pronounced "b cubed".

For more exponents, the expression (for example) $3^5 = 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 = 243$ is called the fifth power of $3$, $3$ raised to the fifth power, or $3$ to the power of $5$.

The word "raised" is usually omitted, and very often "power" as well, so $3^5$ is typically pronounced "three to the fifth" or "three to the five". Therefore, the exponentiation $b^n$ can be read as $b$ raised to the $n-th$ power, or $b$ raised to the power of $n$, or $b$ raised by the exponent of $n$, or most briefly as $b$ to the $n$.



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