Evaluate Each Expression. Write Your Answers As Reduced Fractions.A) $\sqrt{\frac{1}{121}} =$ $\square$B) $-\sqrt{\frac{1}{121}} =$ $\square$

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Introduction

In this article, we will evaluate two expressions involving square roots. We will simplify each expression and write our answers as reduced fractions. The first expression is 1121\sqrt{\frac{1}{121}}, and the second expression is −1121-\sqrt{\frac{1}{121}}.

Simplifying the First Expression

To simplify the first expression, we need to find the square root of 1121\frac{1}{121}. We can start by finding the square root of the numerator and the denominator separately.

Finding the Square Root of the Numerator

The numerator is 1, and the square root of 1 is 1.

Finding the Square Root of the Denominator

The denominator is 121, and we need to find its square root. To do this, we can look for perfect squares that divide 121.

Perfect Squares that Divide 121

The perfect squares that divide 121 are 1, 11, and 121. We can write 121 as 11211^2.

Simplifying the Expression

Now that we have found the square root of the numerator and the denominator, we can simplify the expression.

1121=1121=111\sqrt{\frac{1}{121}} = \frac{\sqrt{1}}{\sqrt{121}} = \frac{1}{11}

Reduced Fraction

The reduced fraction is 111\frac{1}{11}.

Simplifying the Second Expression

To simplify the second expression, we need to find the negative square root of 1121\frac{1}{121}. We can start by finding the negative square root of the numerator and the denominator separately.

Finding the Negative Square Root of the Numerator

The numerator is 1, and the negative square root of 1 is -1.

Finding the Negative Square Root of the Denominator

The denominator is 121, and we need to find its negative square root. To do this, we can look for perfect squares that divide 121.

Perfect Squares that Divide 121

The perfect squares that divide 121 are 1, 11, and 121. We can write 121 as 11211^2.

Simplifying the Expression

Now that we have found the negative square root of the numerator and the denominator, we can simplify the expression.

−1121=−1121=−111-\sqrt{\frac{1}{121}} = -\frac{\sqrt{1}}{\sqrt{121}} = -\frac{1}{11}

Reduced Fraction

The reduced fraction is −111-\frac{1}{11}.

Conclusion

Introduction

In our previous article, we evaluated two expressions involving square roots. We simplified each expression and wrote our answers as reduced fractions. In this article, we will answer some common questions related to evaluating expressions with square roots.

Q: What is the square root of a fraction?

A: The square root of a fraction is the square root of the numerator divided by the square root of the denominator.

Q: How do I simplify a square root of a fraction?

A: To simplify a square root of a fraction, you need to find the square root of the numerator and the denominator separately. Then, you can simplify the expression by dividing the square root of the numerator by the square root of the denominator.

Q: What is the difference between the square root and the negative square root of a fraction?

A: The square root of a fraction is the positive square root of the numerator divided by the positive square root of the denominator. The negative square root of a fraction is the negative square root of the numerator divided by the positive square root of the denominator.

Q: How do I find the negative square root of a fraction?

A: To find the negative square root of a fraction, you need to find the negative square root of the numerator and the positive square root of the denominator. Then, you can simplify the expression by dividing the negative square root of the numerator by the positive square root of the denominator.

Q: What is the reduced fraction of a square root of a fraction?

A: The reduced fraction of a square root of a fraction is the simplified expression with the numerator and denominator in their simplest form.

Q: Can I simplify a square root of a fraction with a variable?

A: Yes, you can simplify a square root of a fraction with a variable. However, you need to follow the same steps as simplifying a square root of a fraction with a constant.

Q: How do I simplify a square root of a fraction with a variable in the denominator?

A: To simplify a square root of a fraction with a variable in the denominator, you need to find the square root of the numerator and the variable in the denominator separately. Then, you can simplify the expression by dividing the square root of the numerator by the square root of the variable in the denominator.

Q: What is the difference between a square root and a negative square root of a fraction with a variable?

A: The square root of a fraction with a variable is the positive square root of the numerator divided by the positive square root of the variable in the denominator. The negative square root of a fraction with a variable is the negative square root of the numerator divided by the positive square root of the variable in the denominator.

Conclusion

In this article, we answered some common questions related to evaluating expressions with square roots. We covered topics such as simplifying square roots of fractions, finding negative square roots of fractions, and simplifying square roots of fractions with variables. We hope that this article has provided you with a better understanding of evaluating expressions with square roots.

Additional Resources

Practice Problems

  • Evaluate the expression 116\sqrt{\frac{1}{16}}.
  • Evaluate the expression −116-\sqrt{\frac{1}{16}}.
  • Simplify the expression x29\sqrt{\frac{x^2}{9}}.
  • Simplify the expression −x29-\sqrt{\frac{x^2}{9}}.