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Chapter 1: Problem 44

\(\sqrt{64}\)

Short Answer

Expert verified
The square root of 64 is 8.

Step by step solution

01

Understand the Problem

Identify what needs to be solved. Here, the task is to find the square root of 64.
02

Recall the Definition

The square root of a number is a value that, when multiplied by itself, gives the original number. Mathematically, if \(\text{a}\) is the square root of \(\text{b}\), then \(\text{a}^2 = \text{b}\).
03

Calculate the Square Root

Find the number that, when multiplied by itself, equals 64. Check if 8 fits this criteria: \(\text{8} \times \text{8} = 64\).
04

Verify the Solution

Ensure that the solution is correct. Since \(\text{8} \times \text{8} = 64\), 8 is indeed the square root of 64.

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Key Concepts

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

Square Root Definition
Square roots are fundamental in mathematics. A square root is a number that produces a specified quantity when multiplied by itself. For example, the square root of 64 is 8 because 8 multiplied by 8 equals 64. Mathematically, we express the square root as follows: If \(a\) is the square root of \(b\), then \(a^2 = b\). This means: 8 * 8 = 64. Square roots can be positive or negative, but when we refer to the square root, typically, we mean the positive root.
Mathematical Verification
Verifying your solution is crucial in mathematics. Verification means checking if your answer is correct. For the square root of 64: Calculate by multiplying 8 by itself. Write it down: \(8 \times 8 = 64\). Observe that this matches the original number you're finding the square root for. Thus, you have verified that 8 is indeed the correct square root of 64. Always verify to ensure accuracy, especially in exams.
Basic Algebra
Understanding square roots involves basic algebra. Algebra is about using symbols (like x or y) to represent numbers. A crucial part of algebra is solving equations. For instance, finding the square root of 64 can be seen as solving the equation \(x^2 = 64\). You need to find x such that \(x \times x = 64\). Knowing algebra helps solve a wide range of mathematical problems, not just square roots. It provides tools to understand how numbers relate to each other.

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Most popular questions from this chapter

An employee works for 8 hours at \(\$ 9.25\) per hour. The employer withholds \(7.65 \%\) of his gross wages for Social Security and Medicare taxes. Find the amount of wages after with holding.

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