Question

What is the exact value of the expression 5 * sqrt 13 + sqrt 6 - 7 *sqrt 13

Answer 1

\[5 \sqrt{13}+\sqrt{6}-7 \sqrt{13} = -\sqrt{2 (29-2 \sqrt{78})} = \sqrt{6}-2 \sqrt{13}\]

Take your pick :-)

The decimal values is about... -4.7616128

Answer 2

All you need to be noticing is that the square roots' of 13 are the same, it's like doing 5x - 7x = -2x