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Write 50 sqrt(-50) in simplest radical form.
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Answer:
50 sqrt(-50) in simplest radical form is 50 i sqrt50i, where i i is the imaginary unit.
Explanation:
We know that the square root of a negative number is an imaginary number. So, to simplify 50 sqrt(-50), we first find the square root of 50 and then multiply it by i i.
To find the square root of 50, we factor it as 50 = 25 × 2 50=25 xx2. Since 25 is a perfect square, we can simplify the square root of 50 as follows:
50 = 25 × 2 = 25 × 2 = 5 2 sqrt50=sqrt(25 xx2)=sqrt25xxsqrt2=5sqrt2
Therefore, 50 = 50 i = 5 2 i sqrt(-50)=sqrt50i=5sqrt2i. This is the simplest radical form of 50 sqrt(-50).
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