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Chapter 8: Problem 42

Simplify the squares and square roots. $$\sqrt{0.09}$$

Short Answer

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0.3

Step by step solution

01

Understand the Problem

The task is to simplify the expression \( \sqrt{0.09} \). This involves finding a number that, when squared, gives 0.09.
02

Express 0.09 as a Square of a Number

Notice that 0.09 can be written as \( \left(0.3\right)^2 \). This is because \( 0.3 \times 0.3 = 0.09 \).
03

Apply the Square Root

Given \( \sqrt{\left(0.3\right)^2} = 0.3 \), we can simplify \( \sqrt{0.09} = 0.3 \).

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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 find a number that, when multiplied by itself, equals the original number. For example, the square root of 9 is 3 because \( 3 \times 3 = 9 \). Square roots can also be applied to decimal numbers, like finding \( \sqrt{0.09} \). In this exercise, we're simplifying \( \sqrt{0.09} \). To do this, we need to find a number that squared equals 0.09.
squares of decimals
Squaring decimals follows the same rules as squaring whole numbers. It involves multiplying the decimal by itself. For instance, \( 0.3 \times 0.3 = 0.09 \). Here, we expressed 0.09 as \( \left(0.3\right)^2 \). This is an essential step because it allows us to apply the square root more easily. Recognizing that 0.09 equals \( \left(0.3\right)^2 \) simplifies finding the square root.
simplifying expressions
Simplifying expressions involves finding a simpler or more intuitive form of a mathematical statement. In this exercise, simplifying \( \sqrt{0.09} \) requires identifying that 0.09 is \( \left(0.3\right)^2 \). Then, taking the square root of \( \left(0.3\right)^2 \) gives us \( 0.3 \). Thus, \( \sqrt{0.09} = 0.3 \). This full process is how we simplify the expression \( \sqrt{0.09} \). Breaking down problems into manageable steps like these ensures that each phase of simplification is clear and understandable.

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