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Chapter 10: Problem 18

Evaluate or simplify each expression. (Assume \(x \geq 0 .)\) $$\sqrt{256}$$

Short Answer

Expert verified
The square root of 256 is 16.

Step by step solution

01

Identify the expression

The given expression is a square root: \( \sqrt{256} \ \).
02

Recall the definition of a square root

The square root of a number is a value that, when multiplied by itself, gives the original number. Therefore, \( \sqrt{256} \ \) is the number that when squared equals 256.
03

Determine the square root of 256

To find the square root of 256, calculate \(256^{0.5} \). Recognize that \( 16 \times 16 = 256 \). Thus, the square root of 256 is \( 16 \).

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Key Concepts

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

square root
Square roots are a fundamental concept in mathematics. They are used to determine what number, when multiplied by itself, equals a given number. For example, the square root of 256 is a number which when squared (multiplied by itself) equals 256.
To find the square root of a number:
  • Identify the number you need to find the square root of.
  • Think of another number which, when multiplied by itself, equals the original number.
  • If you struggle to find it, you can use a calculator for assistance.
Using our example, \( \sqrt{256} \), we recognize that 16 * 16 = 256. So, \( \sqrt{256} = 16 \).
radical expression
A radical expression involves roots of numbers, including square roots, cube roots, and more. The symbol for the square root is \( \sqrt{} \).
Simplifying radical expressions can help better understand their values. For example:
  • Identify the radicand (the number inside the radical sign).
  • Determine the factors of the radicand.
  • From these factors, identify the largest square number.
With \( \sqrt{256} \), since 256 is a perfect square, it simplifies directly to 16. For non-perfect squares, simplify as far as possible while keeping the expression under the radical sign.
evaluating expressions
Evaluating expressions means determining the value of an expression based on the given mathematical operations and numbers. This often involves concepts like square roots and radical expressions.
Steps to evaluate an expression:
  • Identify all numbers and operations in the expression.
  • Follow the order of operations (PEMDAS - Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
  • For square roots and radical expressions, simplify as much as possible and then calculate.
Let's evaluate \( \sqrt{256} \):
  • Recognize that this is a square root operation.
  • Identify \ \sqrt{256} \ and simplify it, noting that 16 * 16 = 256.
  • Thus, \( \sqrt{256} = 16 \).
These steps help break down complex expressions into manageable parts, making it easier to solve and understand.

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Most popular questions from this chapter

Estimate the given square root between two consecutive integers without using a calculator, then use a calculator to find the square root rounded to two decimal places to confirm your estimate. $$\sqrt{872}$$

Perform the indicated operations. Simplify all answers as completely as possible. Assume that all variables appearing under radical signs are nonnegative. $$\frac{10}{4-\sqrt{11}}$$

Factor the given expression as completely as possible. $$x^{2}-6 x$$

Determine whether \(3-\sqrt{13}\) is a solution to the equation \(x^{2}-6 x=3\).

In each of the following, perform the indicated operations and simplify as completely as possible. Assume all variables appearing under radical signs are non negative. $$8 \sqrt{25}-3 \sqrt{21}$$
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