Problem 146 \(-\sqrt{91}\)... [FREE SOLUTION]

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Chapter 10: Problem 146

\(-\sqrt{91}\)

Short Answer

Expert verified

Approximately -9.539.

Step by step solution

Understanding the Problem

We need to find the value of \(-\sqrt{91}\). Let's break it down step by step.

Evaluate the Square Root

First, let's evaluate \(\sqrt{91}\). The square root of 91 is an irrational number that lies between two integers. Use a calculator to find a decimal approximation: \(\sqrt{91} \approx 9.539\).

Apply the Negative Sign

Now, apply the negative sign to the result from Step 1. Hence, \(-\sqrt{91} \approx -9.539\).

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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 us 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 equals 9.
In our exercise, we are trying to find the square root of 91. Unlike 9, 91 is not a perfect square. This means its square root is not an integer, but instead, an irrational number.

An irrational number cannot be expressed as a simple fraction.
Its decimal form goes on forever without repeating.

So, \(\root91\) results in a non-integer. This makes it an irrational number. We use calculators to get a decimal approximation, which is around 9.539 in this case.

Negative Numbers

Negative numbers are numbers less than zero. They are often represented with a minus sign (-).
In our exercise, \(-\sqrt{91}\) means we need to take the positive square root and then apply a negative sign. This changes the value from a positive to a negative.
For instance, if you find that \(\root91\) is approximately 9.539, applying the negative sign gives you -9.539. So, remember: applying the negative sign simply changes the direction on the number line.

Decimal Approximation

Decimal approximation is useful when we deal with irrational numbers or values that cannot be exactly represented.
In our case, we approximated \(\root91\) as 9.539 because it's close to the real value. Calculators usually give us this decimal form.

This is helpful in real-world scenarios where we need a quick, understandable number.
While it's not exact, it's usually close enough for practical purposes.

When you see approximations, remember it's a result rounded to fit neatly into our calculations and understanding. For example, engineers might round decimal numbers to simplify plans.

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91影视

\(-\sqrt{91}\)

Short Answer

Step by step solution

Understanding the Problem

Evaluate the Square Root

Apply the Negative Sign

Key Concepts

Square Roots

Negative Numbers

Decimal Approximation

One App. One Place for Learning.

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