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Chapter 9: Problem 8

Simplify. $$ \sqrt{144} $$

Short Answer

Expert verified
The simplified form of \(\sqrt{144}\) is 12.

Step by step solution

01

Identify the radicand

The radicand is the number inside the square root symbol. In this case, the radicand is 144.
02

Determine the perfect square

Recall the list of perfect squares. Find the perfect square that equals 144. In this case, 12 multiplied by 12 equals 144.
03

Simplify the square root

Since 144 is a perfect square, the square root of 144 is equal to 12. Therefore, \(\sqrt{144} = 12\).

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Key Concepts

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

radicand
The radicand is the number or expression inside the square root symbol (鈭�). In the problem \( \sqrt{144} \), the radicand is 144. Understanding the radicand is crucial because it helps you know what you are finding the square root of.

When you see a root symbol, always check what number or expression is under it. That part tells you what you need to work on to simplify the expression.
perfect squares
Perfect squares are numbers that have whole numbers as their square roots. For instance:
  • 1 is a perfect square because \( 1 \times 1 = 1 \).
  • 4 is a perfect square because \( 2 \times 2 = 4 \).
  • 9 is a perfect square because \( 3 \times 3 = 9 \).


In our problem, 144 is a perfect square because \( 12 \times 12 = 144 \). Recognizing perfect squares quickly makes the process of finding square roots much easier.
simplification
Simplification involves reducing the expression to its simplest form. In our example, we rewrote \(\sqrt{144}\) as 12.

By knowing that 144 is a perfect square and its square root is 12, we can simply state that \( \sqrt{144} = 12 \). Simplification is all about making math easier to handle by breaking it down into straightforward parts. Always look out for perfect squares to make your life simpler.

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