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How do you evaluate #(6+ \sqrt { 7} ) ( 4- \sqrt { 7} )#?

Answer 1

You can use the F.O.I.L. method but that only applies to binomials (such as these). A more general method is to write each term of the first factor as a multiplier of the second factor.

Write each term of the first factor as a multiplier of the second factor:

#(6+ sqrt7) (4-sqrt 7) = 6(4-sqrt7) + sqrt7(4-sqrt7)#

Use the distributive property on both terms of the right side:

#(6+ sqrt7) (4-sqrt 7) = 24-6sqrt7 + 4sqrt7-sqrt7sqrt7#

The last term becomes -7:

#(6+ sqrt7) (4-sqrt 7) = 24-6sqrt7 + 4sqrt7-7#

Combine like terms:

#(6+ sqrt7) (4-sqrt 7) = 17-2sqrt7#

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Answer 2

Savannah Anderson

To evaluate (6+ √7) (4- √7), we can use the distributive property of multiplication.

First, multiply 6 by 4, which gives us 24.

Next, multiply 6 by -√7, which gives us -6√7.

Then, multiply √7 by 4, which gives us 4√7.

Finally, multiply √7 by -√7, which gives us -7.

Now, we can combine these terms:

24 - 6√7 + 4√7 - 7

Simplifying further, we have:

17 - 2√7

Therefore, the evaluation of (6+ √7) (4- √7) is 17 - 2√7.

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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.