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Chapter 1: Problem 23

Evaluate each radical. $$\sqrt{4(7+9)}$$

Short Answer

Expert verified
8

Step by step solution

01

- Simplify the Expression Inside the Radical

First, simplify the expression inside the radical. Start by solving the parentheses: \(7 + 9\).\[7 + 9 = 16\]
02

- Multiply Inside the Radical

Next, multiply the result by 4: \(4 \times 16\).\[4 \times 16 = 64\]
03

- Find the Square Root

Finally, take the square root of the result: \(\sqrt{64}\).\[\sqrt{64} = 8\]

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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 the first and essential step when evaluating radicals.

At this stage, you work on simplifying the mathematical operation inside the radical symbol (鈭�) to make the calculations easier.
For instance, in the expression \(\root(4(7+9))\), we first handle the parentheses (7+9).

We simplify \( 7 + 9 \) to get \( 16 \). Therefore, the expression \( 4(7+9) \) becomes \( 4(16) \).

Understanding how to simplify expressions allows you to focus on more complex parts of the problem. It breaks the calculation into manageable pieces.
multiplication inside radicals
In some math problems, multiplication takes place inside the radical.

Once we have simplified the expression inside the parentheses, we move on to multiplication.
\(\root(4 \times 16)\) \ gets simplified to \( 64 \).

Multiplication inside radicals follows the standard rules of multiplication. The result remains under the radical until you take the square root.

Always ensure the multiplication is accurate to avoid errors in further calculations.
finding square roots
The final step is to find the square root of the number inside the radical.

From the given problem, you take the square root of \( 64 \) which simplifies to 8.

It's helpful to memorize common square roots, like \( 1, 4, 9, 16, 25, 36, 49, 64, 81, \) and \( 100 \), among others.

Recognizing these will make finding square roots quicker and more straightforward.

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Most popular questions from this chapter

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Perform these computations. $$28-0.01$$
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