Evaluate \[$\sqrt{0.72}\$\].

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Introduction

In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number. It is denoted by the symbol $\sqrt{}$. In this article, we will evaluate the square root of 0.72, which is a decimal number. We will use various mathematical techniques to simplify and calculate the square root of 0.72.

Understanding Square Roots

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because 4 multiplied by 4 equals 16. Similarly, the square root of 9 is 3, because 3 multiplied by 3 equals 9. In general, if $x$ is a square root of $y$, then $x^2 = y$.

Evaluating $\sqrt{0.72}$

To evaluate $\sqrt{0.72}$, we can use various mathematical techniques. One way to do this is to simplify the decimal number 0.72 by converting it to a fraction. We can write 0.72 as $\frac{72}{100}$, which can be simplified to $\frac{18}{25}$.

Simplifying the Fraction

Now that we have simplified the decimal number 0.72 to the fraction $\frac{18}{25}$, we can evaluate the square root of this fraction. To do this, we can use the property of square roots that states that the square root of a fraction is equal to the square root of the numerator divided by the square root of the denominator.

Calculating the Square Root

Using the property of square roots mentioned above, we can calculate the square root of $\frac{18}{25}$ as follows:

$$\sqrt{\frac{18}{25}} = \frac{\sqrt{18}}{\sqrt{25}}$$

Simplifying the Square Roots

Now that we have calculated the square root of $\frac{18}{25}$ as $\frac{\sqrt{18}}{\sqrt{25}}$, we can simplify the square roots in the numerator and denominator. We can write $\sqrt{18}$ as $\sqrt{9 \times 2}$, which can be simplified to $3\sqrt{2}$. Similarly, we can write $\sqrt{25}$ as $\sqrt{25}$, which is equal to 5.

Final Calculation

Now that we have simplified the square roots in the numerator and denominator, we can calculate the final value of $\sqrt{0.72}$ as follows:

$$\sqrt{0.72} = \frac{3\sqrt{2}}{5}$$

Conclusion

In this article, we evaluated the square root of 0.72 using various mathematical techniques. We simplified the decimal number 0.72 to the fraction $\frac{18}{25}$ and then used the property of square roots to calculate the square root of this fraction. We simplified the square roots in the numerator and denominator and finally calculated the final value of $\sqrt{0.72}$ as $\frac{3\sqrt{2}}{5}$.

Final Answer

The final answer to the problem $\sqrt{0.72}$ is $\boxed{\frac{3\sqrt{2}}{5}}$.

Related Topics

• Square roots of fractions
• Simplifying square roots
• Properties of square roots

References

• [1] "Square Roots" by Math Open Reference
• [2] "Simplifying Square Roots" by Purplemath
• [3] "Properties of Square Roots" by Khan Academy
  

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Introduction

In our previous article, we evaluated the square root of 0.72 using various mathematical techniques. In this article, we will provide a Q&A guide to help you understand the concept of square roots and how to evaluate them.

Q: What is a square root?

A: A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because 4 multiplied by 4 equals 16.

Q: How do I simplify a decimal number to a fraction?

A: To simplify a decimal number to a fraction, you can write the decimal number as a fraction with a denominator of 10, 100, 1000, and so on. For example, 0.72 can be written as $\frac{72}{100}$, which can be simplified to $\frac{18}{25}$.

Q: How do I evaluate the square root of a fraction?

A: To evaluate the square root of a fraction, you can use the property of square roots that states that the square root of a fraction is equal to the square root of the numerator divided by the square root of the denominator. For example, $\sqrt{\frac{18}{25}} = \frac{\sqrt{18}}{\sqrt{25}}$.

Q: How do I simplify the square roots in the numerator and denominator?

A: To simplify the square roots in the numerator and denominator, you can use the properties of square roots. For example, $\sqrt{18}$ can be written as $\sqrt{9 \times 2}$, which can be simplified to $3\sqrt{2}$. Similarly, $\sqrt{25}$ is equal to 5.

Q: What is the final value of $\sqrt{0.72}$?

A: The final value of $\sqrt{0.72}$ is $\frac{3\sqrt{2}}{5}$.

Q: Can I use a calculator to evaluate the square root of 0.72?

A: Yes, you can use a calculator to evaluate the square root of 0.72. However, it's always a good idea to understand the mathematical techniques behind the calculation.

Q: What are some common mistakes to avoid when evaluating square roots?

A: Some common mistakes to avoid when evaluating square roots include:

• Not simplifying the decimal number to a fraction
• Not using the property of square roots to evaluate the square root of a fraction
• Not simplifying the square roots in the numerator and denominator
• Not checking the final answer for accuracy

Q: How can I practice evaluating square roots?

A: You can practice evaluating square roots by working through examples and exercises in a math textbook or online resource. You can also try evaluating square roots of different numbers to see how the calculations change.

Q: What are some real-world applications of square roots?

A: Square roots have many real-world applications, including:

• Calculating distances and heights in geometry and trigonometry
• Evaluating the area and perimeter of shapes in geometry
• Calculating the volume of objects in physics and engineering
• Evaluating the growth and decay of populations in biology and economics

Conclusion

In this article, we provided a Q&A guide to help you understand the concept of square roots and how to evaluate them. We covered topics such as simplifying decimal numbers to fractions, evaluating the square root of fractions, and simplifying square roots in the numerator and denominator. We also discussed common mistakes to avoid and provided tips for practicing and applying square roots in real-world situations.

Final Answer

The final answer to the problem $\sqrt{0.72}$ is $\boxed{\frac{3\sqrt{2}}{5}}$.

Related Topics

• Square roots of fractions
• Simplifying square roots
• Properties of square roots
• Real-world applications of square roots

References

• [1] "Square Roots" by Math Open Reference
• [2] "Simplifying Square Roots" by Purplemath
• [3] "Properties of Square Roots" by Khan Academy
• [4] "Real-World Applications of Square Roots" by Math Is Fun