We write, for example,

  =  5

"The square root of 25 is 5."

This mark is called the radical sign (after the Latin radix = root). The number under the radical sign is called the radicand.  In the example, 25 is the radicand.

Problem 1.   Evaluate the following.

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a)	=  8		b)	=  12		c)	=  20
d)	=  17		e)	=  1		f)		=	7 9

Rational and irrational numbers

The rational numbers are the numbers of arithmetic:  the whole numbers, fractions, mixed numbers, and decimals; together with their negative images.

That is what a rational number is. As for what it looks

At this point, the student might wonder, What is a number that is not rational?

An example of such a number is ("Square root of 2").   is not a number of arithmetic.  There is no whole number, no fraction, and no decimal whose square is 2.  (1.414 is close, because (1.414)² = 1.999396 -- which is almost 2.)

But to prove that there is no rational number whose square is 2, then

terms. That is, suppose

An equation  x² = a

Example 1.   Solve this equation:

	x²	=	25.
Solution.	x	=	5  or  −5,   because (−5)² = 25, also.
In other words,
	x	=	or  −.

We say however that the positive value 5 is the principal square root. That is, we say that "the square root of 25" is 5.  −5 is "the negative of the square root of 25."

Example 2.   Solve this equation:

	x²	=	10
Solution.	x	=	or  −.

In general, if an equation looks like this,

	x²	=	a
then its solution will look like this:
	x	=	or  −.
We often use the double sign  ± ("plus or minus")  and write:
	x	=	±

Problem 5.   Solve for x.

a)	x² = 9  implies x = ±3		b)	x² = 144  implies x = ±12
c)	x² = 5  implies x = ±		d)	x² = 3  implies x = ±
e)	x² = a − b  implies x = ±