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Chapter 8: Problem 31

Simplify the squares and square roots. $$\sqrt{36}$$

Short Answer

Expert verified
The simplified form of \(\text{\sqrt{36}}\text{ is } 6\).

Step by step solution

01

Identify the Square Root

Recognize that you need to find the square root of the number 36.
02

Find the Perfect Square

Determine if 36 is a perfect square. Since 36 can be written as 6虏, it is indeed a perfect square.
03

Simplify the Square Root

Simplify the square root by taking the number whose square is 36: \(\text{\sqrt{36} = 6}\).

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Key Concepts

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

square roots
Square roots help us find a number that, when multiplied by itself, gives the original number. For example, with \( \sqrt{36} \), we are looking for a number that, when squared (multiplied by itself), equals 36.
To solve this, follow these steps:
  • First, identify what you need to find: the square root of 36.
  • Second, recognize that the square root symbol \( \sqrt{...} \) asks for the number which, when squared, results in the value under the symbol.
  • Finally, find that number, which is 6, because \( 6 \: \times \: 6 = 36 \).

This biological function has many real-life applications, such as determining areas and in various scientific calculations.
perfect squares
Understanding perfect squares is crucial in simplifying square roots. A perfect square is any number that can be expressed as the product of an integer with itself.
Common examples include:
  • 1 (since 1 \(\times\) 1 = 1)
  • 4 (since 2 \(\times\) 2 = 4)
  • 9 (since 3 \(\times\) 3 = 9)
  • 16 (since 4 \(\times\) 4 = 16)
  • 25 (since 5 \(\times\) 5 = 25)
  • 36 (since 6 \(\times\) 6 = 36)

When you see these numbers under a square root symbol, you know that you can simplify them easily to their base numbers. This makes working with square roots more efficient and less time-consuming.
simplifying expressions
Simplifying expressions like \( \sqrt{36} \) involves breaking them down into their simplest forms. Here, since 36 is a perfect square, its simplest form is straightforward: 6.
The process generally involves:
  • Identifying if the number under the square root is a perfect square.
  • If it is, determine the base number. For 36, the base number is 6 since \( 6 \times 6 = 36 \).
  • Express the square root in its simplest form: \( \sqrt{36} = 6 \).

This method can be applied to more complex expressions, making algebraic operations manageable and more understandable. Remember that practicing these steps will help you recognize perfect squares and simplify expressions more quickly.

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