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Math

Math Snap

PROBLEM

Find the following.
6254-\sqrt[4]{625} Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The answer is \square .
B. The root is not a real number.

STEP 1

1. We are asked to find the fourth root of 625 625 and then apply a negative sign.
2. The fourth root of a number x x is a number y y such that y4=x y^4 = x .
3. We need to determine if the result is a real number.

STEP 2

1. Determine the fourth root of 625 625 .
2. Apply the negative sign to the root.
3. Verify if the result is a real number.

STEP 3

Determine the fourth root of 625 625 .
y4=625y^4 = 625 Find y y such that y4=625 y^4 = 625 .

STEP 4

Recognize that 625=54 625 = 5^4 .
Therefore, the fourth root of 625 625 is 5 5 .
6254=5\sqrt[4]{625} = 5

STEP 5

Apply the negative sign to the root.
6254=5-\sqrt[4]{625} = -5

SOLUTION

Verify if the result is a real number.
Since 5 -5 is a real number, the answer is a real number.
The correct choice is:
A. The answer is 5-5.

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