SOLUTION: Evaluate the three radicals. Though they look similar, each one is different. {{{sqrt(16/49)}}} - {{{sqrt(16/49)}}} {{{sqrt(-16/49)}}} -{{{sqrt(-16/49)}}} Which of the abo

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Question 1202968: Evaluate the three radicals. Though they look similar, each one is different.

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Which of the above square roots can be simplified with a real number answer and what is the simplified value?
Which of the above square roots cannot be simplified and why can they not be simplified?

Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!





The square root and squaring exponents cancel out

Through similar steps,


Therefore, the first two items can be simplified to a real number result.

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The last two items cannot be simplified to a real number result because of the negative under the square root.


But if we involve the imaginary number , then we can say

and

Both of these results are complex numbers of the form a+bi

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The reason a negative number is not allowed under the square root is to note how produces nonnegative values when x is a real number.

Examples:
leads to which is nonnegative
leads to which is nonnegative
leads to which is nonnegative
There is no way to have be negative when x is real.

So if then shows that we can only plug in nonnegative values for y.

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