2sqrt6 minus sqrt54 plus fivesqrt24?

Question

find d diference and sum

Answer 1

2sqrt(6) - sqrt(54) + 5sqrt(24)

First, reduce the radicals. Note that
sqrt(54) = sqrt(9*6) = 3sqrt(6), and
sqrt(24) = sqrt(4*6) = 2sqrt(6), so we have

2sqrt(6) - 3sqrt(6) + 5[2sqrt(6)]

2sqrt(6) - 3sqrt(6) + 10sqrt(6)

Now, treat sqrt(6) as a variable.

9sqrt(6)

Answer 2

The answer is 9 sqrt (6), or 22.0450769... . Here's how to show this:

2 sqrt (6) - sqrt (54) + 5 sqrt (24)

= sqrt (6) [2 - sqrt (9) + 5 sqrt (4)]

= sqrt (6) [2 - 3 + 10] = 9 sqrt (6) = 22.0450769...

(It's irrational, of course.)

Live long and prosper.

Answer 3

2√6-√54+5√24
2√6-√(9*6)+5√(4*6)
2√6-3√6+10√6
9√6

Answer 4

2 sqr(6) - sqr(54) + 5 sqr(24)

2 sqr(6) - sqr (2x3x3x3) + 5 sqr(2x2x2x3)

2 sqr(6) - 3 sqr(6) + 5 * 2 sqr(6)

2 sqr(6) - 3 sqr(6) + 10 sqr(6)

9 sqr(6)

sum:

15sqr(6)