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Chapter 5: Problem 5

Evaluate each expression \(\sqrt{64}\)

Short Answer

Expert verified
The square root of 64 is 8.

Step by step solution

01

Understanding the question

The exercise is asking for the square root of 64. The square root of a number is a value that, when multiplied by itself, gives the original number.
02

Calculating the Square Root

The square root of 64 is calculated as follows: \(\sqrt{64} = 8\) because \(8 * 8 = 64\)

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Key Concepts

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

Mathematical Expression
A mathematical expression is a combination of numbers and symbols arranged together to represent a specific value or relation. In this particular exercise, the expression represented is \( \sqrt{64} \)\. The square root symbol, \( \sqrt{} \)\, denotes an operation to find a number which, when multiplied by itself, equals the given value inside the symbol. Here, \( 64 \) is the radicand, which is the number inside the square root symbol you need to evaluate. This means finding a number that, when squared, results in 64.
Arithmetic Calculations
Arithmetic calculations are the procedures we follow to solve problems involving numbers. They include basic operations like addition, subtraction, multiplication, and division. In the context of square roots, it involves finding what number, when multiplied by itself (i.e., squared), equals the number under the square root symbol. For 64, using the principle of squaring, we identify that 8 times 8 results in 64. Therefore, the arithmetic calculation confirms that the square root of 64 is 8.
Problem-Solving Steps
Problem-solving steps are systematic approaches to finding solutions to mathematical questions.
  • First, understand what the problem is asking: here, it's the square root of 64.
  • Next, consider the properties of square roots: a square root seeks a base number that squares to the radicand.
  • Calculate by identifying potential numbers: since 8 times 8 is 64, 8 is confirmed as the square root.
  • Lastly, always verify: check your calculation by squaring the result to ensure accuracy - \( 8 \times 8 = 64 \).

This stepwise approach ensures clarity and correctness in solving mathematical problems.

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Most popular questions from this chapter

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{200}\), when \(a_{1}=60, r=1\).

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(3,15,75,375, \ldots\)

The sum, \(S_{n}\), of the first n terms of an arithmetic sequence is given by $$ S_{n}=\frac{n}{2}\left(a_{1}+a_{n}\right), $$ in which \(a_{1}\) is the first term and \(a_{n}\) is the nth term. The sum, \(S_{n}\), of the first \(n\) terms of a geometric sequence is given by $$ S_{n}=\frac{a_{1}\left(1-r^{n}\right)}{1-r}, $$ in which \(a_{1}\) is the first term and \(r\) is the common ratio \((r \neq 1)\). Determine whether each sequence is arithmetic or geometric. Then use the appropriate formula to find \(S_{10}\), the sum of the first ten terms. \(7,19,31,43, \ldots\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{6}\), when \(a_{1}=-2, r=-3\).

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-1000, r=0.1\)
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