/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 27 Evaluate each radical. $$-2 \s... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 27

Evaluate each radical. $$-2 \sqrt{25+144}$$

Short Answer

Expert verified
-26

Step by step solution

01

Simplify the expression inside the radical

First, add the numbers inside the square root: \[ 25 + 144 = 169 \]
02

Evaluate the square root

Now, find the square root of 169: \[ \sqrt{169} = 13 \]
03

Multiply by the coefficient

Finally, multiply the result by -2: \[ -2 \times 13 = -26 \]

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Key Concepts

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

square root
The square root is a fundamental concept in mathematics where you determine what number, when multiplied by itself, gives the original number. For example, if you have 9, you find that \( \sqrt{9} = 3 \ \) because \( 3 \times 3 = 9 \ \).
It's a key operation to understand because it often appears in various math problems and equations.
In the provided problem, you needed to find the square root of 169. So, \( \sqrt{169} = 13 \ \), since \( 13 \times 13 = 169 \ \).
simplifying expressions
Simplifying expressions means breaking down a math problem into its simplest form. This often involves performing operations inside parentheses first.
In the context of our example, the given expression has numbers inside the square root: \( 25 + 144 \ \). You simplify it by adding the numbers together: \( 25 + 144 = 169 \ \).
Once simplified, you proceed with other operations like taking the square root.
radical multiplication
Radical multiplication involves multiplying numbers that include radicals (square roots). Sometimes, you'll need to multiply coefficients (numbers outside the radical) by the numbers inside the radical.
In our example, once we simplified inside the radical and found \( \sqrt{169} = 13 \ \, \ \), we then had to multiply it by \-2. So, \-2 \times 13 = -26.
This multiplication is straightforward but crucial for correctly evaluating the expression.
basic arithmetic operations
Basic arithmetic operations (addition, subtraction, multiplication, division) are the building blocks of math problems. These operations are often used together in a sequence to solve more complex problems.
In the step-by-step solution, we first performed addition within the radical: \( 25 + 144 = 169 \ \).
Next, we took the square root: \( \sqrt{169} = 13 \ \).
Finally, we multiplied by -2 to obtain the final result: \-2 \times 13 = -26.
Understanding each arithmetic operation helps in successfully evaluating more complicated expressions.

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Most popular questions from this chapter

Simplify each expression. $$ 2\left(-2 x^{2}+1\right)-4\left(x^{2}-3\right)+x^{2} $$

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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

Simplify each expression. $$ a-(4 a-1) $$
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