How do you evaluate 5√1/2 - 2√1/8?

Answer 1
First, #sqrt(1/2) = sqrt(1) / sqrt(2) = 1 / sqrt(2)# and also #sqrt(1/8) = 1 / sqrt(8)#:
#5 * sqrt(1/2) - 2 * sqrt(1/8)# # = 5 / sqrt(2) - 2 / sqrt(8)# # = 5 / sqrt(2) - 2 / sqrt(4*2)# # = 5 / sqrt(2) - 2 / (sqrt(4)*sqrt(2))# # = 5 / sqrt(2) - 2 / (2*sqrt(2))# # = 5 / sqrt(2) - cancel(2) / (cancel(2)*sqrt(2))# # = 5 / sqrt(2) - 1 / sqrt(2)# # = (5 - 1) / sqrt(2)# # = 4 / sqrt(2)#

This might already be the final solution. However, it is nicer not to have any radicals in the denominator, so you could transform it further:

#4 / sqrt(2) = (4 * sqrt(2)) / (sqrt(2) * sqrt(2)) = (4 * sqrt(2)) / 2 = 2 * sqrt(2)#
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Answer 2

To evaluate 5√1/2 - 2√1/8, we can simplify each term separately.

First, let's simplify 5√1/2: √1/2 can be simplified as √(1/2) = √1/√2 = 1/√2. Therefore, 5√1/2 = 5 * (1/√2) = 5/√2.

Next, let's simplify 2√1/8: √1/8 can be simplified as √(1/8) = √1/√8 = 1/√8. Therefore, 2√1/8 = 2 * (1/√8) = 2/√8.

Now, we need to rationalize the denominators of both terms: To rationalize the denominator of 5/√2, we multiply both the numerator and denominator by √2: (5/√2) * (√2/√2) = (5√2)/2.

To rationalize the denominator of 2/√8, we multiply both the numerator and denominator by √8: (2/√8) * (√8/√8) = (2√8)/8.

Now, we can subtract the two terms: (5√2)/2 - (2√8)/8 = (5√2 - 2√8)/2.

This is the simplified form of 5√1/2 - 2√1/8.

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Answer 3

To evaluate 5√(1/2) - 2√(1/8), first simplify each square root:

√(1/2) = √(2/4) = √2 / √4 = √2 / 2 √(1/8) = √(2/16) = √2 / √16 = √2 / 4

Now substitute these simplifications back into the original expression:

5(√2 / 2) - 2(√2 / 4)

Multiply the coefficients with the square roots:

= (5 * √2) / 2 - (2 * √2) / 4

Now, find a common denominator for the fractions:

= (10 * √2) / 4 - (2 * √2) / 4

Combine the fractions:

= (10 * √2 - 2 * √2) / 4

= (8 * √2) / 4

Finally, simplify:

= 2√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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