How do you evaluate 2 square root of 3 - 4 square root of 2 + 6 square root of 3 + 8 square root of 2?

Answer 1

#8sqrt(3)+4sqrt(2)#

#1#. Recall that you can add and subtract radicals if they have the same value in the square root sign. You can think of the #color(teal)("radical")# as a #color(teal)("variable")#. Thus, start by grouping all like terms together.
#color(red)2color(teal)(sqrt(3))# #color(orange)(-4)color(teal)(sqrt(2))# #color(blue)(+6)color(teal)(sqrt(3))# #color(purple)(+8)color(teal)(sqrt(2))#
#=color(red)2color(teal)(sqrt(3))# #color(blue)(+6)color(teal)(sqrt(3))# #color(orange)(-4)color(teal)(sqrt(2))# #color(purple)(+8)color(teal)(sqrt(2))#
#2#. Add/subtract as appropriate.
#=(color(red)2# #color(blue)(+6))color(teal)(sqrt(3))+(color(orange)(-4)# #color(purple)(+8))color(teal)(sqrt(2))#
#3#. Simplify.
#=color(green)(|bar(ul(color(white)(a/a)8sqrt(3)+4sqrt(2)color(white)(a/a)|)))#
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Answer 2

To evaluate the expression 2√3 - 4√2 + 6√3 + 8√2, we can combine like terms.

The terms with the square root of 3 are 2√3 and 6√3, which add up to 8√3.

Similarly, the terms with the square root of 2 are -4√2 and 8√2, which add up to 4√2.

Therefore, the expression simplifies to 8√3 + 4√2.

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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.

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.

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.

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.

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