How do you rationalize the denominator and simplify #2/root4(2)#?

Answer 1

#root(4)(2^3)#

We have to multiply both sides of the division by #sqrt(2^3)#:
#2/root(4)(2)xxroot(4)(2^3)/root(4)(2^3)=(2root(4)(2^3))/root(4)(2xx2^3)#
#=(2root(4)(2^3))/root(4)(2^4)=(2root(4)(2^3))/2=root(4)(2^3)#
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Answer 2

#root(4)(8)#

Given:#" "2/root(4)(2)#
'~~~~~~~~~~~~~~~~~~~~~~~~~ If you have #3sqrt(2)# you may take the 3 inside the squar root as long as you square. So #3sqrt(2)-=sqrt(3^2xx2)#. In the same way if we had #3root(4)(2) -= root(4)(3^4xx2)" "# The three dashes instead of = means equivalent to. '~~~~~~~~~~~~~~~~~~~~~~~~~~~

Applying this idea we have

#root(4)(2^4/2) = root(4)(2^3) = root(4)(8)#
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Answer 3

To rationalize the denominator and simplify 2/√4(2), we can follow these steps:

  1. Simplify the square root: √4 = 2.
  2. Rewrite the expression as 2/2√2.
  3. Divide both the numerator and denominator by 2: 2/2 = 1.
  4. The simplified form is 1/√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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