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How do you simplify #sqrt(1+x) + sqrt(1-x)#?

Answer 1

You square the equation and solve normally. The answer is 2.

Since both parts of the equation are being square rooted you can square the whole equation to turn #sqrt(1+x) + sqrt(1-x)# to #1+x+1-x#. Your then solve that expression normally to get you final answer.

Step by step: #sqrt(1+x) + sqrt(1-x)# #1+x+1-x# #1+1+x-x# Now we conbine the x's and ones to get our final answer of #2#

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Answer 2

Genesis Allen

To simplify sqrt(1+x) + sqrt(1-x), we can use the formula for the sum of square roots. By squaring the expression, we can eliminate the square roots.

(sqrt(1+x) + sqrt(1-x))^2 = (1+x) + 2(sqrt(1+x))(sqrt(1-x)) + (1-x)

Simplifying further, we have:

= 2 + 2(sqrt(1+x))(sqrt(1-x))

Therefore, sqrt(1+x) + sqrt(1-x) cannot be simplified further.

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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.