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Chapter 9: Problem 8

Evaluate the expression. $$\sqrt{36}$$

Short Answer

Expert verified
The square root of 36 is 6.

Step by step solution

01

Identify the Number

Identify the number that you need to find the square root of, which in this case is 36.
02

Find the Square Root

Find the square root of 36. The square root of 36 is a number which when squared, or multiplied by itself, results in the number 36. That number is 6 because \(6 \times 6 = 36\).

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Key Concepts

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

Evaluating Expressions
Evaluating expressions involves performing mathematical operations to find the value of the given expression. With square roots, you are often tasked with finding a number that can be multiplied by itself to achieve the original number under the square root symbol. When encountering \(\sqrt{36}\), you must determine the number that, when squared, equals 36. This process is crucial for simplifying expressions and solving equations.
  • The expression \(\sqrt{36}\) requires determining what number times itself equals 36.
  • Mental computation or basic multiplication skills can assist in quickly identifying this number.
Identifying the number correctly sets the foundation for simplifying the entire expression.
Basic Arithmetic Operations
Understanding basic arithmetic operations such as addition, subtraction, multiplication, and division is essential, especially when dealing with square roots. Multiplication plays a key role in identifying the square root. The square root of a number is essentially the reverse operation of squaring a number. For the number 36:
  • You are asked to perform the multiplication operation backwards to find its square root.
  • You test various numbers: for example, multiply 5 by itself (\(5 \times 5\)), which equals 25, or 7 by itself (\(7 \times 7\)), which equals 49.
  • Recognize that 6 multiplied by itself (\(6 \times 6\)) results in 36.
Such number manipulation helps in swiftly arriving at the correct square root.
Number Identification
Number identification is a critical step when evaluating mathematical expressions like square roots. It refers to recognizing and understanding the properties of numbers involved in operations. With \(\sqrt{36}\), you are identifying 36 as the number whose square root needs determination:
  • Recognizing 36 as a perfect square makes identifying its square root straightforward.
  • Familiarize yourself with common perfect squares such as 1 (\(1 \times 1 = 1\)), 4 (\(2 \times 2 = 4\)), 9 (\(3 \times 3 = 9\)), and so on up to higher perfect squares.
  • Number identification also involves understanding why certain numbers are termed perfect squares, helping you quickly calculate or estimate square roots in the future.
Grasping these concepts enhances overall mathematical fluency and problem-solving skills.

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Most popular questions from this chapter

Evaluate \(\sqrt{b^{2}-4 a c}\) for the given values. $$a=-3, b=7, c=5$$

Sketch the graph of the function. Label the vertex. y=-2 x^{2}-3 x+2

SOLVING INEQUALITIES Solve the inequality. $$\frac{x}{6} \leq-2$$

Use a calculator to evaluate the expression. Round the results to the nearest hundredth. $$\frac{6 \pm 4 \sqrt{2}}{-1}$$

Solve the equation or write no solution. Write the solutions as integers if possible. Otherwise write them as radical expressions. $$x^{2}-7=57$$
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