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Chapter 8: Problem 5

Solve. \(\sqrt{(8)(2)}\)

Short Answer

Expert verified
4

Step by step solution

01

Understand the Expression

The given expression is \( \sqrt{(8)(2)} \). This expression represents the square root of the product of 8 and 2.
02

Multiply the Numbers Inside the Square Root

Calculate the product of 8 and 2: \( 8 \cdot 2 = 16 \). So the expression becomes \( \sqrt{16} \).
03

Calculate the Square Root

Find the square root of 16: \( \sqrt{16} = 4 \).

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Key Concepts

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

multiplication
Multiplication is one of the basic arithmetic operations and involves combining equal groups. For example, when you multiply 8 by 2, you're essentially adding 8 twice: 8 + 8. This action results in the product of 16. Multiplication is frequently used in algebra and helps in simplifying expressions, especially when dealing with square roots and radicals. To multiply two numbers, you simply need to know your multiplication facts or use repeated addition.
radicals
Radicals often involve square roots, cube roots, or higher. In this exercise, we're dealing with the square root, which is a special kind of radical. A square root asks: 'What number, when multiplied by itself, gives the original number?' For instance, the square root of 16 asks: 'What number times itself equals 16?' And the answer is 4, because 4 * 4 = 16. Radicals can simplify complex expressions: for example, \( \sqrt{(8)(2)} \) first becomes \( \sqrt{16} \). Understanding how to manipulate and simplify radicals helps solve a variety of algebraic problems.
basic algebra
Basic algebra is foundational for advanced math. It involves using letters (variables) to represent numbers, enabling you to solve equations and understand mathematical relationships. In this solution, we use basic algebra to understand and simplify the expression \( \sqrt{(8)(2)} \). First, we multiply the numbers 8 and 2, resulting in 16. Then, finding the square root of 16 yields 4. Basic algebra often requires knowledge of arithmetic operations like multiplication and understanding radical expressions. This allows for simplification and solving equations efficiently.

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Most popular questions from this chapter

Simplify the following radical expressions by factoring. \(\sqrt{27}\)

Change the exponential expressions into radical expressions. \(10^{\frac{1}{2}}\)

Solve each of the following square root problems by rewriting the radical expression as two separate expressions. \(\sqrt{(4)(11)}\)

Solve. \(2 \sqrt{3}-4 \sqrt{3}\)

In each of the following, add or subtract the radical expressions. \(5 \sqrt{2 x}-2 \sqrt{2 x}\)
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