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Chapter 9: Problem 1

Simplify. $$ \sqrt{100} $$

Short Answer

Expert verified
The simplified form of \( \sqrt{100} \) is 10.

Step by step solution

01

Identify the Radicand

The radicand is the number inside the square root symbol. For this problem, the radicand is 100.
02

Find the Square Root

Determine which number, when multiplied by itself, equals the radicand. We need to find the number that satisfies: \( x^2 = 100 \).
03

Solve for x

Solving the equation \( x^2 = 100 \), we find that \( x = 10 \) because \( 10 \times 10 = 100 \).

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Key Concepts

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

Radicand
The radicand is a fundamental concept in square root problems. It is the number or expression inside the square root symbol, also known as the radical sign.
In our exercise, the radicand is 100. When we see \( \sqrt{100} \), 100 is the number we need to focus on to find its square root.
Understanding the radicand helps us identify which number we need to work with. It sets the stage for the rest of our problem-solving steps.
Square Root
The square root is the number that, when multiplied by itself, results in the original radicand.
For example, the square root of 100 is the number that satisfies the equation \( x^2 = 100 \).
It's essential to recognize that each positive number has both a positive and a negative square root. However, when we refer to 'the square root,' we usually mean the positive root.
Hence, for the radicand 100, the square root is 10 because \( 10 \times 10 = 100 \).
Multiplication
Multiplication plays a crucial role when dealing with square roots. To verify the solution to our square root problem, we use multiplication.
By taking our square root (which is 10 in the case of \( \sqrt{100} \)), we can multiply it by itself to see if we return to the original radicand:
\( 10 \times 10 = 100 \).
This multiplication confirms that our square root finding is correct. This step of verification ensures our solution is precise and correct.
Basic Mathematics
Understanding basic mathematics is crucial for grasping square roots and similar problems.
Concepts such as identifying the radicand, finding the square root, and performing multiplication are foundational.
Simplifying square roots, like \( \sqrt{100} \), is an excellent exercise in applying these basic mathematical principles.
Strengthening these skills ensures students have a robust mathematical foundation for more complex topics in the future.

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