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Chapter 3: Problem 19

Tell whether each computation is correct or incorrect. $$ \sqrt{3}-\sqrt{0}=\sqrt{3} $$

Short Answer

Expert verified
The computation is correct.

Step by step solution

01

Examine Each Term Inside the Square Root

Identify the terms inside the square root. Here, it involves \(\sqrt{3}\) and \(\sqrt{0}\).
02

Simplify \(\sqrt{0}\)

Calculate \(\sqrt{0}\): Since the square root of zero is zero, \(\sqrt{0}=0\).
03

Perform the Subtraction

Subtract the values obtained from the square roots: \(\sqrt{3} - \sqrt{0} = \sqrt{3} - 0 = \sqrt{3}\).
04

Verify Equality

Compare the result from Step 3 with the original expression. Since \(\sqrt{3} - 0 = \sqrt{3}\), the equality \(\sqrt{3} - \sqrt{0} = \sqrt{3}\) holds true.

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Key Concepts

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

Simplifying Square Roots
Basic arithmetic operations are fundamental to understanding more complex math concepts. In the given problem, subtraction is used. Let's break this down:
- Identify the terms involved. Here, \[ \sqrt{3} \] and \[ \sqrt{0} \] are our two square roots.
- Understand that subtraction is about finding the difference.

When simplifying \[ \sqrt{0} \], it is zero, as highlighted before. This makes the subtraction operation straightforward: \[ \sqrt{3} - \sqrt{0} = \sqrt{3} - 0 = \sqrt{3} \].

Therefore, understanding subtraction here simplifies our problem.
Verifying Equality
Finally, let's verify the equality. Verifying means ensuring that both sides of the equation are the same. For the problem: \[ \sqrt{3} - \sqrt{0} = \sqrt{3} \], we already simplified it to convert to \[ \sqrt{3} \]. Since this was straightforward and didn鈥檛 change, both sides are equal.

Rechecking the terms shows the same value:
- The left side: \[ \sqrt{3} - 0 \]
- The right side: \[ \sqrt{3} \]

Conclusion: \(\backslash \sqrt{3} \) throughout, verifying the equality.

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Most popular questions from this chapter

For this problem, assume \(x\) is positive. a. Name three values of \(x\) for which \(\sqrt{x}\) is less than \(x\) . b. Name three values of \(x\) for which \(\sqrt{x}\) is greater than \(x\) . c. In general, how can you tell whether \(\sqrt{x}\) is greater than \(x ?\)

The diameter of the body of a Purkinje cell is \(8 \times 10^{-5} m\) a. If a microscope magnifies 1,000 times, what will be the scaled diameter, in meters, as viewed in the microscope? b. What is the scaled diameter, in centimeters, as viewed in the microscope?

Julia found three Web sites that sell 4-inch-square stickers of her favorite band鈥檚 logo. The three sites sell the stickers for different prices, and charge different amounts for shipping. Site \(1 :\) Stickers are 75 each; shipping is \(\$ 4\) for any size order. Site \(2 :\) Stickers are 60\(\phi\) each; shipping is \(\$ 5.50\) for any size order. Site \(3 :\) Stickers are \(\$ 1.25 ;\) shipping is included. a. For each site, write an equation to represent the charge \(C\) for ordering any number of stickers \(s\) b. Graph your three equations on axes like these. Label each graph with its site number. c. Use your graph to answer this question: If Julia wants to order 16 stickers, which site will charge her the least? d. Use your graph to answer this question: If Julia wants to order 10 stickers, which site will charge her the least?

Solve each equation. If it has no solution, write "no solution." $$ 5 \sqrt{x}=25 $$

Solve each equation. If it has no solution, write "no solution." $$ \sqrt{x+2}+8=1 $$
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