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Chapter 9: Problem 17

Find the indicated principal or negative square root, if possible. $$\sqrt{100}$$

Short Answer

Expert verified
The square root of 100 is 10.

Step by step solution

01

Understand the Concept of Square Root

The square root refers to a number, which, when squared (multiplied by itself), will result in the initial number. The sign 鈭� is used to denote the square root.
02

Apply the Definition of Square Root

Since the number is 100, you need to find a number which when multiplied by itself gives 100. That number is 10, because 10*10 equals 100.
03

Write down the Answer

Therefore, the square root of 100 is 10.

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Key Concepts

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

Understanding Principal Square Root
When we talk about square roots, we often refer to the *principal square root*. This is the non-negative square root of a number. For any positive number, there are always two possible square roots: a positive one and a negative one. However, the principal square root focuses on the positive value.
For instance, in the case of the number 100, the square roots are +10 and -10. But the principal square root is only +10. This is because, by convention, the principal square root symbol \( \sqrt{ } \) is understood to represent the positive root.
  • The principal square root of a non-negative number is always non-negative.
  • It is denoted by the radical symbol without any sign.
  • The principal square root of 100 is \( \sqrt{100} = 10 \).
The Role of Perfect Squares
A perfect square is a number that can be expressed as the product of an integer with itself. In simpler terms, if you can find an integer that squares to a given number, then that number is a perfect square.
For example, 100 is a perfect square because it equals 10 times 10. Perfect squares are always the result of squaring whole numbers, and they always yield nice, whole number roots. This makes them very straightforward when calculating square roots.
  • Common perfect squares include numbers like 1, 4, 9, 16, 25, and 100.
  • Recognizing perfect squares can make root calculations quick and easy.
  • Perfect squares are important for their simplicity in mathematical operations.
Exploring Radical Notation
Radical notation is a way of expressing roots of numbers. When you see the symbol \( \sqrt{ } \), it is called the radical symbol, and it signifies the root operation.
  • The number under the radical symbol is known as the radicand. For example, in the expression \( \sqrt{100} \), 100 is the radicand.
  • Radical notation can express square roots, cube roots, and higher roots, though square roots are the most common.
  • To determine the radical value, identify the number which can be multiplied by itself to produce the radicand.
Using radical notation is helpful because it gives a clear, visual way to express roots which is especially useful in algebra and higher math. The radical symbol has now become a universal part of expressing various root values, helping people easily communicate root operations in mathematics.

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