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Chapter 0: Problem 41

Find each square root. If it is not a real number, say so. $$ \sqrt{81} $$

Short Answer

Expert verified
The square root of 81 is 9.

Step by step solution

01

Understand the Problem

The goal is to find the square root of 81. A square root of a number is a value that, when multiplied by itself, gives the original number.
02

Identify Perfect Squares

Determine if 81 is a perfect square. A perfect square is a number that can be expressed as the square of an integer.
03

Calculation

Calculate the square root of 81. Find an integer such that multiplying it by itself results in 81.
04

Solution Verification

Verify the calculation: Determine if the integer found in the previous step is correct by squaring it to see if it equals 81.

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Key Concepts

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

Perfect Square
To start, let's understand what a perfect square is. A perfect square is a number that can be expressed as the square of an integer. This means if you can find a whole number that, when multiplied by itself, equals the original number, then you have a perfect square. For example, 81 is a perfect square because it can be written as 9 multiplied by 9, or mathematically, \(9^2 = 81\). Knowing about perfect squares helps to identify if a number has a neat, whole-number square root.
Integer
An integer is a whole number that can be positive, negative, or zero. Integers include numbers like -2, -1, 0, 1, 2, etc. They do not include fractions or decimals. When determining if a number is a perfect square, we check if there is an integer that can be squared to give us that number. For instance, with 81, the integer 9 satisfies this condition because when squared, it gives 81.
Calculation
Calculating the square root involves identifying an integer that, when multiplied by itself, equals the given number. In simpler terms, it is finding a number which squares back to the original number. For the number 81, we think about which integer, when multiplied by itself, equals 81. We find that \(9 \times 9 = 81\) which means that \(\text{鈭�81 = 9}\). This step requires practice and familiarity with multiplication and perfect squares.
Verification
Verification is crucial in ensuring your solution is correct. Once you find a candidate integer, you must square it to confirm it equals the original number. For example, if we found 9 as the square root of 81, we verify it by squaring 9. We check this by calculating \(9 \times 9\) which indeed equals 81. This confirmation step ensures no mistakes were made in finding the square root. Always verify to make sure the solution is accurate and complete.

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Most popular questions from this chapter

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