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Chapter 1: Problem 24

Evaluate each radical. $$\sqrt{(11+2)(18-5)}$$

Short Answer

Expert verified
13

Step by step solution

01

- Simplify the expression inside the parenthesis

Start by simplifying each expression inside the parenthesis: \(11 + 2 = 13\) and \(18 - 5 = 13\).
02

- Multiply the results

Multiply the simplified results from step 1: \(13 \times 13 = 169\).
03

- Evaluate the square root

Evaluate the square root of the result from step 2: \( \sqrt{169} = 13\).

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Key Concepts

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

Simplifying Expressions
Simplifying expressions involves reducing them to their simplest form. It makes calculations easier and helps in understanding the core concept. In the exercise given, we need to simplify two expressions inside the parentheses: \((11 + 2)\text{ and }(18 - 5)\). \ The steps required to simplify these expressions are: \
    \
  • Simplify each individual part within the parentheses.
    • \
  • \text{For} \(11 + 2\), we add 11 and 2 to get 13.
    • \
  • \text{For} \(18 - 5\)), we subtract 5 from 18 to get 13.
    • \
\ Simplifying expressions is the first step towards solving any complex algebraic problem and sets the stage for further operations.
Multiplication
In the context of this exercise, once we have simplified the expressions inside the parentheses, the next step is to multiply the results. Multiplication is a fundamental arithmetic operation. Here's how we proceed: \ Consider our simplified expressions from the previous step: 13 and 13. \ We now multiply these values: \ \[13 \times 13 = 169\] \ Understanding how to multiply numbers correctly is vital because multiplication often serves as a building block for more complex mathematics, including algebra and calculus.
Square Roots
After simplifying and multiplying, the final step is to evaluate the square root of the result. A square root of a number is a value which, when multiplied by itself, gives the original number. For instance, the square root of 169 is 13 because: \ \[13 \times 13 = 169\] \ In this exercise, after simplifying and multiplying to get 169, we take the square root: \ \[ \sqrt{169} = 13 \] \ Square roots are essential in various fields of mathematics, including geometry, algebra, and more advanced calculus. Properly understanding this operation is crucial for tackling a myriad of mathematical problems.

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Most popular questions from this chapter

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