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How do you simplify #5 sqrt48- 8 sqrt 27#?

Answer 1

Emery Allen

#5sqrt48-8sqrt27=-4sqrt3#

#5sqrt48-8sqrt27#

= #5sqrt(2xx2xx2xx2xx3)-8sqrt(3xx3xx3)#

= #5sqrt(ul(2xx2)xxul(2xx2)xx3)-8sqrt(ul(3xx3)xx3)#

Remove the squared values from the square root.

= #5xx2xx2xxsqrt3-8xx3xxsqrt3#

= #20sqrt3-24sqrt3#

= #-4sqrt3#

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Answer 2

Luna Angel

To simplify (5\sqrt{48} - 8\sqrt{27}), first, factor the numbers inside the square roots:

(48 = 16 \times 3) and (27 = 9 \times 3).

Then, simplify the square roots:

(\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3})

(\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3})

Now, substitute these simplified forms back into the expression:

(5\sqrt{48} - 8\sqrt{27} = 5(4\sqrt{3}) - 8(3\sqrt{3}))

Simplify further:

(= 20\sqrt{3} - 24\sqrt{3})

Now, combine like terms:

(= (20 - 24)\sqrt{3})

Finally, calculate the result:

(= -4\sqrt{3})

So, (5\sqrt{48} - 8\sqrt{27}) simplifies to (-4\sqrt{3}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.