Given that c is a prime number, rationalise the denominator of 3c-√c / √c. Simplify the answer.

Question

Given that c is a prime number, rationalise the denominator of 3c-√c / √c. Simplify the answer.

Answer 1

as written it's

=3c -(sqrc/sqrc)

= 3c -sqrc/sqrc

= 3c -1

but maybe you really meant to write

(3c-sqrc)/sqrc then multiply both numerator and denominator by sqrc

=(3csqrc - c)/c

= 3sqrc - 1

= 3 times the square root of c minus one

the point of c being prime is that you can't leave sqr(c) in the denominator if it's to be rational. Only square root of a perfect square is a rational number. square root of a prime number is an irrational number. sqr2 = about 1.414... with decimals that go on forever, and never repeat. if it's a rational number it will repeat at some point.