Problem 48 Determine whether the statement ... [FREE SOLUTION]

Chapter 0: Problem 48

Determine whether the statement is true or false. $$-7<-\sqrt{7}$$

Short Answer

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True

Step by step solution

Understand the Problem

The problem is to determine if the statement $-7 < -\sqrt{7}$ is true or false. This requires comparing the values of $-7$ and $-\sqrt{7}$.

Evaluate the Square Root

$\sqrt{7}$ represents the positive square root of 7. Calculate $~\sqrt{7}$, which approximately equals 2.64575.

Negate the Square Root

Negate the value found in Step 2: $-\sqrt{7} \approx -2.64575$.

Compare the Values

Compare $-7$ with $-\sqrt{7}$. Since $-7$ is less than $-2.64575$, the inequality $-7 < -\sqrt{7}$ is true.

Conclusion

The statement $-7 < -\sqrt{7}$ is true.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

comparing values

In algebra, comparing values is a fundamental skill. It involves determining which of two numbers is larger or smaller. When we compare negative numbers, the one with the smaller absolute value is actually the larger number. For example, $-2$ is greater than $-5$ because $-2$ is closer to zero. Similarly, in our problem, we compare $-7$ and $-\sqrt{7}$. Remember that the negative sign means both numbers are less than zero. However, because \sqrt{7}\ is approximately 2.64575, \-\sqrt{7}\ is approximately \-2.64575. Since $-7$ is further from zero than \-2.64575\, $-7 < -\sqrt{7}$\ is true.

square roots

The square root of a number $n$ is a value $y$ such that $y^2=n$. In other words, if you multiply $y$ by itself, you get $n$. For example, the square root of 9 is 3 because $3脳3=9$. The symbol for the square root is $\sqrt{}$. In our problem, we have the square root of 7, which is denoted as $\sqrt{7}$. This value lies between 2 and 3 because $2^2=4$ and $3^2=9$. More precisely, $\sqrt{7}$ is roughly equal to 2.64575. Square roots can be found using a calculator or estimated for simpler values.

negation of numbers

Negating a number means changing its sign. If the number is positive, its negation is negative, and vice versa. For example, the negation of 5 is \-5\, and the negation of $-3)\ is 3. In our problem, we start with \(\sqrt{7}$, which is approximately 2.64575, and we negate it to get $-\sqrt{7}$. After negation, \{-\sqrt{7}=\approx -2.64575\). This step is crucial in comparing the initial value with its negated form. By understanding how to negate numbers, you can easily manipulate and compare both positive and negative values.

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91影视

Determine whether the statement is true or false. $$-7<-\sqrt{7}$$

Short Answer

Step by step solution

Understand the Problem

Evaluate the Square Root

Negate the Square Root

Compare the Values

Conclusion

Key Concepts

comparing values

square roots

negation of numbers

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