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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