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How do you simplify #(2sqrt2 + 2sqrt24) * sqrt3#?

Answer 1

Roman Alvarez

#(2sqrt2+2sqrt24)*sqrt3=2sqrt6+12sqrt2#

#(2sqrt2+2sqrt24)*sqrt3#

= #2sqrt2*sqrt3+2sqrt24*sqrt3#

and as #sqrtaxxsqrtb=sqrtab#, this is equal to

#2sqrt6+2sqrt72#

= #2sqrt(2xx3)+2sqrt(ul(2xx2)xx2xxul(3xx3))#

= #2sqrt6+12sqrt2#

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Answer 2

Riley Anderson

To simplify ( (2\sqrt{2} + 2\sqrt{24}) \times \sqrt{3} ):

Use the distributive property to multiply ( \sqrt{3} ) with each term inside the parentheses.
( (2\sqrt{2} \times \sqrt{3}) + (2\sqrt{24} \times \sqrt{3}) )
Simplify the square roots inside each term:

( 2\sqrt{6} + 2\sqrt{72} )
Simplify the square root of 72:

( 2\sqrt{6} + 2\sqrt{36} )
Since ( \sqrt{36} = 6 ), the expression becomes:

( 2\sqrt{6} + 2 \times 6 )
Simplify:

( 2\sqrt{6} + 12 )

So, ( (2\sqrt{2} + 2\sqrt{24}) \times \sqrt{3} ) simplifies to ( 2\sqrt{6} + 12 ).

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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.