Math / Numbers & Operations

QuestionFind the following. $-\sqrt[4]{625}$
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.

Studdy Solution

STEP 1

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

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

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

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QuestionFind the following. $-\sqrt[4]{625}$
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.

Studdy Solution

STEP 1

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

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

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

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QuestionFind the following. −6254-\sqrt[4]{625}−4625​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.

Studdy Solution

STEP 1

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

STEP 2

1. Determine the fourth root of 625 625 625.2. Apply the negative sign to the root.3. Verify if the result is a real number.

STEP 3

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

STEP 4

Recognize that 625=54 625 = 5^4 625=54.Therefore, the fourth root of 625 625 625 is 5 5 5.6254=5\sqrt[4]{625} = 54625​=5

STEP 5

Apply the negative sign to the root.−6254=−5-\sqrt[4]{625} = -5−4625​=−5

STEP 6

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

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QuestionFind the following. $-\sqrt[4]{625}$
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.

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

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

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

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

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

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