If I tell you that the square root of 2 (for example) is such-and-such, you can verify this by multiplying the number by itself, and seeing whether the result is close to 2.
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because 2 times 2 = 4
Most high school algebra books show a proof (by contradiction) that the square root of 2 is irrational. The same proof can easily be adapted to the square root of any positive integer, that is not a perfect square. You can find the proof (for the square root of 2) on the Wikipedia article on "irrational number", near the beginning of the page (under "History").
Since the square root of a number is the "number times itself that equals the original number," it makes sense that the larger the original number, then the larger the square root. The value of the square root of 2 will be greater than the value of the square root of 1.5.
The square root of a value v is a number x such that, x multiplied by x equals v. Note that -x is also a square root.
It is no tpossible to find the square root of an unknown number. You can, however, represent it as x0.5 or √x so that the value of the square root can be evaluated when the value of x is known.