Problem 496 In the following exercises, simp... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 5: Problem 496

In the following exercises, simplify. $$ -\sqrt{121} $$

Short Answer

Expert verified

-11

Step by step solution

- Identify the Square Root

First, identify the square root of the number inside the radical. In this case, the number inside the square root is 121. The square root of 121 is 11 because 11 * 11 equals 121.

- Apply the Negative Sign

After finding the square root, apply the negative sign outside the radical. Since the square root of 121 is 11, applying the negative sign gives: -11.

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Key Concepts

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

Understanding Square Roots

Square roots are one of the fundamental concepts in mathematics. A square root is a number that, when multiplied by itself, results in the original number. For example, the square root of 121 is 11 because 11 multiplied by 11 equals 121. To express square roots, we use the radical symbol $\sqrt{}$. The number under the square root symbol is called the radicand.
Here are a few key points about square roots:

Every positive number has two square roots: a positive and a negative one. For instance, 16 has square roots 4 and -4.
The square root of a perfect square (like 121, 144, 169) is always an integer.
Most numbers are not perfect squares, so their square roots are irrational numbers (like $\sqrt{2}$ or $\sqrt{3}$).

Knowing these basics will help you simplify and understand square roots better.

Dealing with Radicals

Radicals are expressions that involve roots, such as square roots, cube roots, and so on. The most common radical is the square root, represented by $\sqrt{}$. When simplifying expressions with radicals, consider the following steps:
Identify the radicand: The number under the radical.
Find the root: For square roots, look for a number which, when squared, equals the radicand.
Simplify the expression: Once you find the root, rewrite the expression without the radical if possible.

For example, $\sqrt{49} = 7$ because 7 * 7 = 49.
For non-perfect squares, you can leave the expression in its radical form, such as $\sqrt{2}$.

Radicals can sometimes include variables or negative numbers, adding a layer of complexity. Understanding radical expressions and their simplifications is an essential skill in algebra and higher math.

Negative Numbers and Square Roots

Handling square roots with negative numbers can be tricky because the result of a square root operation is always non-negative. However, if there's a negative sign outside the radical, like in the exercise $-\sqrt{121}$, it means that after calculating the square root, you apply the negative sign to the result.
Key points to remember:

Square roots of positive numbers are always non-negative.
Square roots of negative numbers are not defined within the set of real numbers. They involve imaginary numbers, expressed as $i$, where $i = \sqrt{-1}$.
When a negative sign is outside a square root (like $-\sqrt{121}$), you first find the square root as usual (11 in this case) and then apply the negative sign to get -11.

This means that $-\sqrt{121} = -11$. It's crucial to distinguish between the negative sign inside the square root (which leads to imaginary numbers) and the negative sign outside (which simply makes the final result negative).

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91影视

In the following exercises, simplify. $$ -\sqrt{121} $$

Short Answer

Step by step solution

- Identify the Square Root

- Apply the Negative Sign

Key Concepts

Understanding Square Roots

Dealing with Radicals

Negative Numbers and Square Roots

One App. One Place for Learning.

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