Which Expression Is Equivalent To $\sqrt{100}$?A. 10 B. $10^2$ C. 50 D. $50^2$

When dealing with mathematical expressions, it's essential to understand the concepts of square roots and exponents. A square root of a number is a value that, when multiplied by itself, gives the original number. On the other hand, an exponent is a number that represents the power to which a base number is raised. In this article, we will explore which expression is equivalent to $\sqrt{100}$.

What is a Square Root?

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because 4 multiplied by 4 equals 16. The square root of a number is denoted by the symbol $\sqrt{}$. In the given problem, we are asked to find the equivalent expression for $\sqrt{100}$.

Understanding Exponents

An exponent is a number that represents the power to which a base number is raised. For example, $2^3$ means 2 raised to the power of 3, which equals 8. Exponents can be used to simplify complex expressions and make them easier to work with. In the given problem, we are asked to compare the given options with the expression $\sqrt{100}$.

Analyzing the Options

Let's analyze the given options and compare them with the expression $\sqrt{100}$.

Option A: 10

The square root of 100 is a value that, when multiplied by itself, gives 100. Since 10 multiplied by 10 equals 100, option A is a possible equivalent expression for $\sqrt{100}$.

Option B: $10^2$

The expression $10^2$ means 10 raised to the power of 2, which equals 100. This expression is equivalent to the square root of 100, because both expressions equal 100.

Option C: 50

The square root of 100 is a value that, when multiplied by itself, gives 100. Since 50 multiplied by 50 does not equal 100, option C is not a possible equivalent expression for $\sqrt{100}$.

Option D: $50^2$

The expression $50^2$ means 50 raised to the power of 2, which equals 2500. This expression is not equivalent to the square root of 100, because it equals a different value.

Conclusion

In conclusion, the expression equivalent to $\sqrt{100}$ is $10^2$. This expression equals 100, which is the same value as the square root of 100. The other options do not equal the square root of 100, and therefore are not equivalent expressions.

Key Takeaways

• A square root of a number is a value that, when multiplied by itself, gives the original number.
• An exponent is a number that represents the power to which a base number is raised.
• The expression equivalent to $\sqrt{100}$ is $10^2$.
• The other options do not equal the square root of 100, and therefore are not equivalent expressions.

Final Answer

In the previous article, we discussed the concept of square roots and exponents, and how to find the equivalent expression for $\sqrt{100}$. In this article, we will answer some frequently asked questions (FAQs) about square roots and exponents.

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

A: A square root of a number is a value that, when multiplied by itself, gives the original number. On the other hand, an exponent is a number that represents the power to which a base number is raised. For example, the square root of 16 is 4, because 4 multiplied by 4 equals 16. The exponent $2^3$ means 2 raised to the power of 3, which equals 8.

Q: How do I simplify a square root expression?

A: To simplify a square root expression, you need to find the largest perfect square that divides the number inside the square root. For example, $\sqrt{16}$ can be simplified as $\sqrt{4 \times 4}$, which equals 4.

Q: What is the relationship between square roots and exponents?

A: The square root of a number is equivalent to raising that number to the power of 1/2. For example, $\sqrt{16}$ is equivalent to $16^{1/2}$, which equals 4.

Q: How do I evaluate an expression with a square root and an exponent?

A: To evaluate an expression with a square root and an exponent, you need to follow the order of operations (PEMDAS). For example, $\sqrt{16^2}$ can be evaluated as follows:

1. Evaluate the exponent: $16^2 = 256$
2. Take the square root: $\sqrt{256} = 16$

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

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

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

A: The square root of a negative number is an imaginary number, which is a complex number that cannot be represented on the real number line. For example, the square root of -16 is an imaginary number, which can be represented as $4i$, where $i$ is the imaginary unit.

Q: What is the relationship between square roots and logarithms?

A: The square root of a number is equivalent to the logarithm of that number with a base of 2. For example, $\sqrt{16}$ is equivalent to $\log_2{16}$, which equals 4.

Conclusion

In conclusion, we have answered some frequently asked questions (FAQs) about square roots and exponents. We hope that this article has provided you with a better understanding of these concepts and how to apply them in different situations.

Key Takeaways

• A square root of a number is a value that, when multiplied by itself, gives the original number.
• An exponent is a number that represents the power to which a base number is raised.
• The square root of a negative number is an imaginary number.
• The square root of a number is equivalent to raising that number to the power of 1/2.
• The square root of a number is equivalent to the logarithm of that number with a base of 2.

Final Answer

The final answer is $\boxed{10^2}$.