Question

Evaluate \(100^{\frac{1}{2}}\). A. 50 B. 10 C. \(\frac{1}{200}\) D. \(\frac{1}{10,000}\)

Short answer

B. 10

Step-by-step solution

Understand the Expression

The expression given is \(100^{\frac{1}{2}}\). This represents the square root of 100.

Compute the Square Root

Recall that the square root of a number \(x\) is a value that, when multiplied by itself, gives \(x\). In this case, \(\sqrt{100} = 10\), because \(10 \times 10 = 100\).

Identify the Correct Answer

From the previous step, we found that \(100^{\frac{1}{2}} = 10\). Thus, the correct answer is B. 10.

Key concepts

Square Root

When evaluating expressions with exponents, it's essential to understand square roots. The square root of a number is a value that, when multiplied by itself, yields the original number. For example, the square root of 100 is 10. This is because multiplying 10 by 10 results in 100; symbolically, \(\text{10} \times \text{10} = 100\). In mathematical terms, this can be represented as \(\text{{\backslash sqrt{100} = 10}}\). Recognizing that \(100^{1/2}\) is the same as \(\text{{\backslash sqrt{100}}}\) is a key insight that helps simplify and evaluate these expressions accurately.

Exponentiation

Exponentiation is a fundamental concept in mathematics where a number (the base) is raised to the power of an exponent. This operation indicates repeated multiplication. For instance, \(2^{3} = 2 \times 2 \times 2 = 8\). An important special case of exponentiation is when the exponent is \(1/2\), which signifies taking the square root of the base. Therefore, \(\text{{100^{1/2}}}\) equivalently means finding the square root of 100, which yields 10. Remembering this property helps in evaluating and simplifying expressions quickly.

Simplifying Expressions

Simplifying mathematical expressions is a crucial skill. It involves reducing an expression to its simplest form. To simplify \(100^{1/2}\), we recognize it represents the square root of 100. By computing that the square root of 100 is 10, the original expression simplifies to 10. Here are some tips for simplifying expressions:

• Identify special exponent properties, such as \(x^{1/2}\) being the square root of \x\.
• Break down the expression step-by-step to avoid errors.
• Write out the intermediate steps for clarity.

Consistent practice will enhance your ability to simplify expressions effortlessly.