Why did it make mathematically sense to rationalize the denominator that has the square root symbol?

Question

Please include the source of information:

Thank You

Answer 1

By rationalizing a square root number in a denominator, you can then divide it into any rational factor in the numerator, and get rid of the fraction line. For example, suppose you have the fraction 15/root 3. Multiply top and bottom by root 3, and you get 15*root3/3. Now you can divide the 3 into the 15, leaving you with a simplified answer of 5*root3. Secondly, if you need an actual decimal number for your answer, it's a lot easier to multiply by an approximation of root 3 (1.7321, say) than it is to divide by such a number.

Answer 2

That was true when there were no calculators and computers; to make calculations easier. Today, it is not really necessary to do this if you want to get the value of a fraction with a square root or any root in the denominator. It is just to make
the expression look good or the simplication of an expression easier if required. No reference. Just experience from teaching math for 30 yrs hehehhe. So that's it. I think for the ancient people, it was easier to multiply a square root than to use it as a divisor using logarithms. Forget it. Use your calculator. (Unless of course you're dealing with algebraic fractions that you need to simplify.)

These are the sort of things that make students hate math. :-)

Answer 3

Because to effectively compute a division problem, one needs the divisor to be an integer, and if the denominator of a fraction is not rational, then that would be difficult.

Answer 4

That's a good question. It doesn't make mathematical sense. Could be teachers think it looks neater.
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Answer 5

We don't like to divide by expression with square root signs.

http://faculty.ed.umuc.edu/~swalsh/Math%20Articles/Rationalize.html

Answer 6

Because your teacher/instructor told you to.