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Chapter 1: Problem 28

Evaluate each radical. $$-3 \sqrt{169-144}$$

Short Answer

Expert verified
-15

Step by step solution

01

Simplify the expression inside the square root

First, simplify the expression inside the square root. Calculate the difference: $$169 - 144 = 25.$$
02

Evaluate the square root of the simplified expression

Next, find the square root of the result from Step 1. $$\text{The square root of } 25 \text{ is } \sqrt{25} = 5.$$
03

Multiply by the coefficient

Finally, multiply the result of the square root by the coefficient -3. $$-3 \times 5 = -15.$$

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Key Concepts

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

simplifying expressions
Simplifying expressions is an important skill in math. It involves reducing complex expressions to their simplest form. When evaluating radicals, simplifying expressions typically means cleaning up what's inside the square root first.

For example, in our exercise, we start with simplifying the inside of the square root: \[169 - 144 = 25\]By performing this subtraction, we reduce \ the expression to a simpler version.
square roots
Square roots are a fundamental concept in math too. The square root of a number 'x' is a value 'y' such that \[y^2 = x\]. For instance, \[ \text{the square root of } 25 \text{ is } 5\]because \[5^2 = 25\]. When evaluating the square root of 25, you identify the number that, when squared, gives you 25. In routines involving more complex numbers, simplifying the expression inside the square root, as we did in the first step, greatly helps find the result.
multiplication with coefficients
Multiplication with coefficients is the last step in our solution. Coefficients are numbers that multiply a variable or a result. In our case, the coefficient is -3, which we use to multiply the square root result.

Thus, we multiply: \[\text{-3} \times 5 = -15\].

Always remember this step: after evaluating the inner expression and finding its square root, apply the coefficient to get the final result.

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Most popular questions from this chapter

Solve each problem. Cooperative learning The sum of the integers from 1 through \(n\) is \(\frac{n(n+1)}{2}\) The sum of the squares of the integers from 1 through \(n\) is \(\frac{n(n+1)(2 n+1)}{6} .\) The sum of the cubes of the integers from 1 through \(n\) is \(\frac{n^{2}(n+1)^{2}}{4} .\) Use the appropriate expressions to find the following values. a) The sum of the integers from 1 through 50 b) The sum of the squares of the integers from 1 through 40 c) The sum of the cubes of the integers from 1 through 30 d) The square of the sum of the integers from 1 through 20 e) The cube of the sum of the integers from 1 through 10

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