Problem 34 \(-\sqrt{196}\)... [FREE SOLUTION]

Chapter 10: Problem 34

\(-\sqrt{196}\)

Short Answer

Expert verified

鈭�14

Step by step solution

Identify the Square Root

Begin by identifying the square root of the number inside the radical. Here, the number is 196. The positive square root of 196 is found by determining which number, when multiplied by itself, equals 196. The number is 14 since \(14 \times 14 = 196\).

Apply the Negative Sign

Next, apply the negative sign in front of the square root that we just calculated. Since the square root of 196 is 14, the expression becomes \(-14\).

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Key Concepts

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

Negative Square Root

When you see a negative sign in front of a square root, it means you take the negative value of the number inside the square root. For example, in \(-\sqrt{196}\), the negative sign tells us to find the square root of 196 and then apply the negative sign to the result.
To break it down:

First, find the positive square root of the number inside the radical, which in this case is 196. The square root of 196 is 14 because \(14 \times 14 = 196\).
Then, apply the negative sign in front of 14, resulting in -14.

This is different from a positive square root where we simply take the square root without applying a negative sign. So, always remember that the negative in front of a square root makes the final value negative.

Radical Expressions

Radical expressions involve roots, such as square roots. The radical symbol \(\sqrt{}\) is used to indicate a root.

When you see \(\sqrt{x}\), it implies finding a number that, when squared (or raised to the power of 2), equals \(x\).

For instance, \(\sqrt{49} = 7\) because \(7 \times 7 = 49\). Radical expressions can also involve higher roots, like cube roots, but square roots are the most common.
Inside a radical, you can have numbers and variables. For example, \(\sqrt{25} = 5\) and \(\sqrt{x^2} = x\).
This means you often encounter these in algebra when solving equations or simplifying expressions.

Basic Algebra Operations

Basic algebra operations are foundational skills that you use to solve equations and simplify expressions. These include:

Addition and subtraction
Multiplication and division
Exponentiation
Roots (such as square roots)

For example, in the given problem \(-\sqrt{196}\), we use:

Exponentiation to understand that 196 is 14 squared (\(14^2\))
Root (square root in this case) operation to find that \(\sqrt{196} = 14\)
Subtraction, in the form of applying the negative sign to get -14

You can think of algebra as a language of symbols and rules that let us solve for unknowns and understand relationships between different elements.

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\(-\sqrt{196}\)

Short Answer

Step by step solution

Identify the Square Root

Apply the Negative Sign

Key Concepts

Negative Square Root

Radical Expressions

Basic Algebra Operations

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