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Chapter 10: Problem 38

Evaluate or simplify each expression. (Assume \(x \geq 0 .)\) $$\sqrt{100}-\sqrt{36}$$

Short Answer

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4

Step by step solution

01

- Evaluate the Square Roots

Find the square root of each number. The square root of 100 is 10, and the square root of 36 is 6.
02

- Substitute the Values

Replace the square roots with their evaluated values. The expression becomes: \[ \sqrt{100} - \sqrt{36} = 10 - 6 \]
03

- Simplify the Expression

Subtract the values to simplify the expression. \[ 10 - 6 = 4 \]

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Key Concepts

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

Square Roots
Square roots are a fundamental concept in algebra. They represent a value that, when multiplied by itself, gives the original number. For example, the square root of 100 is 10 because \(10 \times 10 = 100\). Similarly, the square root of 36 is 6 because \(6 \times 6 = 36\). Understanding square roots is essential for evaluating and simplifying various mathematical expressions.
Working with square roots often involves:
  • Identifying the perfect squares.
  • Using prime factorization for larger numbers.
  • Remembering common square roots like \( \sqrt{1} = 1, \sqrt{4} = 2.\)

When starting to find the square root, it鈥檚 helpful to think of the number you are squaring. Practicing this skill will help in solving more complex algebraic problems.
Evaluating Expressions
Evaluating expressions is about calculating the numerical value of an algebraic expression. In our example, we need to evaluate the expression \( \sqrt{100} - \sqrt{36} \). We start by evaluating each component of the expression separately:
  • First, calculate \( \sqrt{100} = 10 \).
  • Next, calculate \( \sqrt{36} = 6 \).

After finding these values, substitute them back into the original expression to get: \( 10 - 6 \). This process shows how we can simplify an expression step by step to find its value.
Simplifying Expressions
Simplifying expressions in algebra means reducing them to their simplest form. This is achieved by performing arithmetic operations and combining like terms. In our exercise, after evaluating the square roots, we ended up with the expression \( 10 - 6 \).
To simplify the expression:
  • Subtract 6 from 10.
  • This gives us the simplified result of 4.

It is helpful to remember that simplifying expressions often involves:
  • Performing basic arithmetic operations.
  • Combining like terms.
  • Following the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

By applying these principles, you can simplify even complex expressions more easily.

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Most popular questions from this chapter

Perform the indicated operations and simplify. $$\frac{3}{2 x}+\frac{5}{x+2}$$

Factor the given expression as completely as possible. $$w^{3}-8 w^{2}+16 w$$

Perform the indicated operations. Simplify all answers as completely as possible. Assume that all variables appearing under radical signs are nonnegative. $$\frac{\sqrt{5}}{\sqrt{6}-\sqrt{5}}$$

Perform the indicated operations. Simplify all answers as completely as possible. Assume that all variables appearing under radical signs are nonnegative. $$\frac{8}{\sqrt{a}-\sqrt{2}}$$

Sketch the graph of each equation in a rectangular coordinate system. Label the intercepts. $$5 y-2 x=10$$
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