Solved on Feb 22, 2024

Find the negative square root of $\frac{4}{81}$ . Express the answer as a proper fraction, improper fraction, or whole number.

STEP 1

Assumptions
1. We need to find the negative square root of the fraction $\frac{4}{81}$ .
2. The result should be expressed as a proper fraction, improper fraction, or whole number.

STEP 2

The square root of a fraction can be found by taking the square root of the numerator and the denominator separately.
$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

STEP 3

Apply this property to the given fraction.
$\sqrt{\frac{4}{81}} = \frac{\sqrt{4}}{\sqrt{81}}$

STEP 4

Calculate the square root of the numerator and the denominator.
$\sqrt{4} = 2$ $\sqrt{81} = 9$

STEP 5

Substitute the square roots back into the fraction.
$\sqrt{\frac{4}{81}} = \frac{2}{9}$

STEP 6

Since we are looking for the negative square root, we add a negative sign to the result.
$-\sqrt{\frac{4}{81}} = -\frac{2}{9}$
The negative square root of $\frac{4}{81}$ is $-\frac{2}{9}$ .

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Find the negative square root of $\frac{4}{81}$ . Express the answer as a proper fraction, improper fraction, or whole number.

STEP 1

Assumptions
1. We need to find the negative square root of the fraction $\frac{4}{81}$ .
2. The result should be expressed as a proper fraction, improper fraction, or whole number.

STEP 2

The square root of a fraction can be found by taking the square root of the numerator and the denominator separately.
$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

STEP 3

Apply this property to the given fraction.
$\sqrt{\frac{4}{81}} = \frac{\sqrt{4}}{\sqrt{81}}$

STEP 4

Calculate the square root of the numerator and the denominator.
$\sqrt{4} = 2$ $\sqrt{81} = 9$

STEP 5

Substitute the square roots back into the fraction.
$\sqrt{\frac{4}{81}} = \frac{2}{9}$

STEP 6

Since we are looking for the negative square root, we add a negative sign to the result.
$-\sqrt{\frac{4}{81}} = -\frac{2}{9}$
The negative square root of $\frac{4}{81}$ is $-\frac{2}{9}$ .

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Find the negative square root of 481\frac{4}{81}814​. Express the answer as a proper fraction, improper fraction, or whole number.

STEP 1

Assumptions1. We need to find the negative square root of the fraction 481\frac{4}{81}814​.2. The result should be expressed as a proper fraction, improper fraction, or whole number.

STEP 2

The square root of a fraction can be found by taking the square root of the numerator and the denominator separately.ab=ab\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}ba​​=b​a​​

STEP 3

Apply this property to the given fraction.481=481\sqrt{\frac{4}{81}} = \frac{\sqrt{4}}{\sqrt{81}}814​​=81​4​​

STEP 4

Calculate the square root of the numerator and the denominator.4=2\sqrt{4} = 24​=2 81=9\sqrt{81} = 981​=9

STEP 5

Substitute the square roots back into the fraction.481=29\sqrt{\frac{4}{81}} = \frac{2}{9}814​​=92​

STEP 6

Since we are looking for the negative square root, we add a negative sign to the result.−481=−29-\sqrt{\frac{4}{81}} = -\frac{2}{9}−814​​=−92​The negative square root of 481\frac{4}{81}814​ is −29-\frac{2}{9}−92​.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the negative square root of $\frac{4}{81}$ . Express the answer as a proper fraction, improper fraction, or whole number.

Assumptions
1. We need to find the negative square root of the fraction $\frac{4}{81}$ .
2. The result should be expressed as a proper fraction, improper fraction, or whole number.

The square root of a fraction can be found by taking the square root of the numerator and the denominator separately.
$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

Apply this property to the given fraction.
$\sqrt{\frac{4}{81}} = \frac{\sqrt{4}}{\sqrt{81}}$

Calculate the square root of the numerator and the denominator.
$\sqrt{4} = 2$ $\sqrt{81} = 9$

Substitute the square roots back into the fraction.
$\sqrt{\frac{4}{81}} = \frac{2}{9}$

Since we are looking for the negative square root, we add a negative sign to the result.
$-\sqrt{\frac{4}{81}} = -\frac{2}{9}$
The negative square root of $\frac{4}{81}$ is $-\frac{2}{9}$ .