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Chapter 9: Problem 80

\(\sqrt{(-6)^{2}-4(1)(9)}\)

Short Answer

Expert verified
\(\sqrt{(-6)^{2}-4(1)(9)}=0\).

Step by step solution

01

Identify the expression inside the square root

The given expression is \(\text{inside the square root:} (-6)^{2}-4(1)(9)\).
02

Calculate the value of \((-6)^{2}\)

Calculate the square of -6: \((-6)^{2} = 36\).
03

Calculate the value of \(-4(1)(9)\)

Calculate the product of -4, 1, and 9: \(-4(1)(9) = -36\).
04

Combine the results

Combine the results from steps 2 and 3: \(36 - 36 = 0\).
05

Take the square root of the result

Calculate the square root of 0: \(\text{The square root of 0 is }\sqrt{0}=0\).

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Key Concepts

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

evaluating expressions
Evaluating expressions can seem difficult at first, but when you break it down into simpler steps, the process becomes much easier. In this exercise, we are given the expression \(\sqrt{(-6)^{2}-4(1)(9)}\)\. The goal is to simplify this expression step by step. First, identify the operations and numbers involved: we have a square of -6, multiplication of -4, 1, and 9, and then their combination under a square root.

Breaking down the expression into smaller parts helps make it manageable and allows for easier computation. Always work inside out when handling square root problems or similar nested expressions.
square roots
Square roots are a fundamental concept in mathematics, and they often appear in various problems, from simple arithmetic to advanced calculus. The square root of a number is a value that, when multiplied by itself, gives the original number. For example, \( \sqrt{16} = 4 \) because \( 4 \times 4 = 16\)\.

In our exercise, after simplifying the expression inside the square root, we get 0. Therefore, the square root of 0 is \(\sqrt{0} = 0\)\. Remember, square roots can only be taken of non-negative numbers, which makes understanding and working with them an essential skill in mathematics.
step-by-step solutions
Approaching problems with step-by-step solutions is an excellent strategy for mastering mathematical concepts. Let's revisit the given problem and see how each step builds on the previous one to simplify the expression and find the final answer.

  • Step 1: Identify the expression inside the square root: \( (-6)^{2}-4(1)(9) \)\.
  • Step 2: Calculate \(\(-6)^{2} = 36 \).
  • Step 3: Calculate \(\-4(1)(9) = -36 \).
  • Step 4: Combine the results of steps 2 and 3: \36 - 36 = 0 \).
  • Step 5: Take the square root of the result: \(\sqrt{0} = 0 \).
This methodical approach not only simplifies complex problems but also systematically builds your understanding and proficiency with mathematical operations.

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Most popular questions from this chapter

\(3 b^{2}-11 b+1=0\)

Explain why the square root of a negative number cannot be a real number.

\(v^{2}+6 v+3=0\)

Wal-Mart advertised a Thanksgiving dinner for a family of eight for under \(\$ 20\), not including tax. The dinner included a 12 -pound turkey at \(\$ 0.40\) per pound, three cans of vegetables at \(\$ 0.50\) each, 2 lb of sweet potatoes at \(\$ 0.25\) per pound, two cans of cranberries at \(\$ 0.88\) each, one 12 -count package of brown and serve rolls for \(\$ 0.75\), two packages of stuffing mix at \(\$ 1.50\) each, and one pumpkin roll cake at \(\$ 5.50\). In Idaho, the sales tax on food is \(6.5 \%\). Find the total cost of the dinner, including tax. Round to the nearest hundredth.

\(d^{2}-15=0\)
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