Evaluate − 4 C − 6 A B -\sqrt{4c - 6ab} − 4 C − 6 Ab ​ When A = − 2 A = -2 A = − 2 , B = 8 B = 8 B = 8 , And C = 1 2 C = \frac{1}{2} C = 2 1 ​ . Write Your Answer In Simplest Form And In Decimal Form Rounded To The Nearest Hundredth.Simplest Form: □ \square □ Decimal Form: About

Introduction

In this article, we will evaluate the expression $-\sqrt{4c - 6ab}$ when $a = -2$, $b = 8$, and $c = \frac{1}{2}$. We will first substitute the given values into the expression and then simplify it to find the simplest form. Finally, we will round the result to the nearest hundredth to obtain the decimal form.

Substituting the Given Values

To evaluate the expression, we need to substitute the given values of $a$, $b$, and $c$ into the expression. We have:

$a = -2$ $b = 8$ $c = \frac{1}{2}$

Substituting these values into the expression, we get:

$-\sqrt{4\left(\frac{1}{2}\right) - 6(-2)(8)}$

Simplifying the Expression

Now, we need to simplify the expression inside the square root. We have:

$4\left(\frac{1}{2}\right) - 6(-2)(8)$

Using the order of operations (PEMDAS), we first multiply the numbers inside the parentheses:

$4\left(\frac{1}{2}\right) = 2$ $6(-2)(8) = -96$

Now, we can simplify the expression further:

$2 - (-96)$

Using the rule that $a - (-b) = a + b$, we can rewrite the expression as:

$2 + 96$

Now, we can simplify the expression further:

$98$

So, the expression inside the square root simplifies to $98$.

Evaluating the Square Root

Now, we need to evaluate the square root of $98$. We have:

$-\sqrt{98}$

To evaluate the square root, we can use the fact that $\sqrt{ab} = \sqrt{a}\sqrt{b}$. However, in this case, we can simply find the square root of $98$ and then multiply it by $-1$.

Using a calculator, we can find that $\sqrt{98} \approx 9.90$. Therefore, we have:

$-\sqrt{98} \approx -9.90$

Conclusion

In this article, we evaluated the expression $-\sqrt{4c - 6ab}$ when $a = -2$, $b = 8$, and $c = \frac{1}{2}$. We first substituted the given values into the expression and then simplified it to find the simplest form. Finally, we rounded the result to the nearest hundredth to obtain the decimal form.

Simplest Form

The simplest form of the expression is:

$-\sqrt{98}$

Decimal Form

The decimal form of the expression is approximately:

$-9.90$

Final Answer

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Introduction

In our previous article, we evaluated the expression $-\sqrt{4c - 6ab}$ when $a = -2$, $b = 8$, and $c = \frac{1}{2}$. We found that the simplest form of the expression is $-\sqrt{98}$ and the decimal form is approximately $-9.90$. In this article, we will answer some frequently asked questions related to the evaluation of the expression.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an expression inside a square root?

A: To simplify an expression inside a square root, we need to follow the order of operations. We first evaluate any expressions inside parentheses, then any exponential expressions, and finally any multiplication and division operations. After that, we can simplify the expression further by combining any like terms.

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

A: A square root is a number that, when multiplied by itself, gives a specified value. For example, the square root of 16 is 4, because 4 multiplied by 4 equals 16. A negative square root is a number that, when multiplied by itself, gives a negative value. For example, the negative square root of 16 is -4, because -4 multiplied by -4 equals 16.

Q: How do I evaluate a square root expression with a negative number inside the square root?

A: To evaluate a square root expression with a negative number inside the square root, we need to follow the order of operations. We first evaluate any expressions inside parentheses, then any exponential expressions, and finally any multiplication and division operations. After that, we can simplify the expression further by combining any like terms. If the number inside the square root is negative, we can rewrite it as a positive number by multiplying it by -1.

Q: What is the decimal form of a square root expression?

A: The decimal form of a square root expression is a decimal approximation of the square root. To find the decimal form of a square root expression, we can use a calculator to evaluate the square root and then round the result to the nearest hundredth.

Q: How do I round a decimal to the nearest hundredth?

A: To round a decimal to the nearest hundredth, we need to look at the thousandth place (the third digit after the decimal point). If the thousandth place is 5 or greater, we round up the hundredth place. If the thousandth place is less than 5, we round down the hundredth place.

Conclusion

In this article, we answered some frequently asked questions related to the evaluation of the expression $-\sqrt{4c - 6ab}$. We covered topics such as the order of operations, simplifying expressions inside a square root, the difference between a square root and a negative square root, and how to evaluate a square root expression with a negative number inside the square root. We also covered how to find the decimal form of a square root expression and how to round a decimal to the nearest hundredth.

Final Answer

The final answer is: $\boxed{-9.90}$