Simplify :

a) -6 square root (80) + 2 square root (75) - 8 suqare root (245) -14 square root (108)

Perform the indicated operation.

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-6 (sqrt 80) + 2 (sqrt 75) - 8 (sqrt 245) - 14 (sqrt 108)

Factoring:

-6 (sqrt 2*2*2*2*5) + 2 (sqrt 3*5*5) - 8 (sqrt 5*7*7) - 14 (sqrt 2*2*3*3*3)

Pulling out the squares:

(-6*2*2)(sqrt 5) + (2*5)(sqrt 3) - (8*7)(sqrt5) - (14*2*3)(sqrt 3)

Simplify:

-24 (sqrt 5) + 10 (sqrt 3) - 56 (sqrt 5) - 84 (sqrt 3)

Combine like terms:

(-24-56)(sqrt 5) + (10-84)(sqrt 3)

Simplify:

-80 (sqrt 5) - 74 (sqrt 3)

Hope this helps. Good luck!

We need to simplify the numbers inside the radical by factoring out any perfect squares.

= -6 sqrt(16*5) + 2 sqrt(25*3) - 8 sqrt(49*5) - 14 sqrt(36*3)

= -6*4*sqrt(5) + 2*5*sqrt(3) - 8*7*sqrt(5) - 14*6*sqrt(3)

= -24 sqrt(5) + 10 sqrt(3) - 56 sqrt(5) - 84 * sqrt(3)

Now we simplify by combining like terms, in this case terms with the same numbers inside the radical.

= (-24 - 56) sqrt(5) + (10 - 84) sqrt(3)

and we get the final answer of

= -80 sqrt(5) - 74 sqrt(3)

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