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Question: Use radical notation to rewrite the expression. Simplify, if possible. 2561/4-256^{1/4} Select…

Use radical notation to rewrite the expression. Simplify, if possible.

2561/4-256^{1/4}

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. 2561/4=0-256^{1/4} = \boxed{\phantom{0}}

B. The root is not a real number.

Solution

To solve the problem of rewriting 2561/4 -256^{1/4} in radical notation, we first interpret the expression and consider whether it represents a real number. The given expression is: 2561/4 -256^{1/4} In radical form, this is expressed as: (2561/4)=2564 -(256^{1/4}) = -\sqrt[4]{256} Now, we determine if 2564\sqrt[4]{256} is a real number. First, find the fourth root of 256: 2561/4=4 256^{1/4} = 4 Therefore: (2561/4)=4 -(256^{1/4}) = -4 Thus, the answer is: A. 2561/4=4 -256^{1/4} = -4 This option is correct, as the root is a real number.

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