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Chapter 10: Problem 34

Find each square root, if possible. $$-\sqrt{\frac{1}{100}}$$

Short Answer

Expert verified
The square root of the given expression is: \(-\sqrt{\frac{1}{100}} = -0.1\).

Step by step solution

01

Convert the fraction to a decimal

First, let's convert the fraction inside the square root to a decimal: \[\frac{1}{100} = 0.01\]
02

Calculate the square root of the decimal

Now, we want to find the square root of 0.01: \[\sqrt{0.01} = 0.1\]
03

Consider the negative sign outside the square root

Let's multiply the square root value by the negative sign outside the square root: \[-\sqrt{0.01} = -0.1\] So, the result is: \[-\sqrt{\frac{1}{100}} = -0.1\]

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Key Concepts

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

Converting Fractions to Decimals
Fractions and decimals are two ways to represent numbers. Some students might find decimals easier to work with, especially when dealing with square roots. To convert a fraction to a decimal, you simply divide the numerator (the top number) by the denominator (the bottom number). In our exercise, we have the fraction \( \frac{1}{100} \).
  • Divide 1 by 100.
  • The result is 0.01.

It鈥檚 important to understand this concept because working with decimals, when possible, simplifies calculations, especially when using calculators for finding square roots.
Decimals are more intuitive for many people and can make it easier to understand the size and scale of a number.
Understanding Negative Numbers
Negative numbers can be a bit tricky, especially when they're outside a square root. But don鈥檛 worry, it's quite simple once you break it down!
  • A negative number is just the opposite of a positive number.
  • For example, if 5 is 5 units to the right of zero on a number line, then -5 is 5 units to the left.

In our exercise,
  • We found the square root of the decimal (\( \sqrt{0.01} = 0.1 \)).
  • The negative sign outside means we take that positive result and flip it to the negative, giving us -0.1.

Negative signs outside of square roots simply change positive results into negative ones, keeping in line with basic arithmetic rules.
Simplifying Radicals
Simplifying radicals involves breaking down the number under the square root into its simplest form. This helps to make calculations easier and the results more precise. To simplify a radical:
  • Look for perfect squares inside the radical.
  • When a perfect square is found, you can take it out of the radical.

For example, with \( \sqrt{100} \):
  • 100 is a perfect square (\(10 \times 10 \)).
  • You can simplify \( \sqrt{100} \) to 10.
In our exercise, we first simplified \( \sqrt{\frac{1}{100}} \) by converting \(\frac{1}{100}\) to a decimal \(0.01\), then found \( \sqrt{0.01} = 0.1 \). With this approach, simplifying the problem step by step made the solution clear and accessible.

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Most popular questions from this chapter

Rationalize the denominator of each expression. $$\frac{1}{\sqrt{5}}$$

Rationalize the denominator and simplify completely. Assume the variables represent positive real numbers. $$\frac{5}{4+\sqrt{6}}$$

What does it mean to rationalize the denominator of a radical expression?

Multiply and simplify. $$\sqrt{\frac{6}{5}} \cdot \sqrt{\frac{1}{8}}$$

Multiply and simplify. $$\sqrt{\frac{6}{7}} \cdot \sqrt{\frac{7}{3}}$$
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