Problem 50 Find the indicated principal or ... [FREE SOLUTION]

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Elementary Algebra Within Reach

Ron Larson, Kimberly Nolting

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 10: Problem 50

Find the indicated principal or negative $n$th root. $$-\sqrt{900}$$

Short Answer

Expert verified

The negative square root of 900 is -30.

Step by step solution

Identify the number

The number given is 900, and a negative sign precedes the square root. So, it is required to find the negative root of 900.

Find the square root

The square root of 900 is calculated by finding a number which, when multiplied by itself, gives 900. In this case, that number is 30 because $30 \times 30 = 900$.

Apply the negative sign

Since the problem is to find a negative square root, and 30 is the square root of 900, the negative square root of 900 is -30.

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Key Concepts

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

Square Root Calculation

Square root calculation involves finding a number which, when multiplied by itself, results in the original number. For example, in the case of 900, the goal is to find a number such that when squared gives 900. To do so, you can perform trial and error or use direct calculation methods. The square root of 900 is 30 because multiplying 30 by itself gives 900: \[30 \times 30 = 900\]Square roots can often be found using a calculator or by memorizing common square roots, like those of perfect squares. For non-perfect squares, approximation methods may be necessary.

Negative Numbers

Negative numbers are an integral part of mathematics, representing values less than zero. In the context of roots, a negative square root means finding the square root of a number and then applying a negative sign to it. For instance, if you take the square root of 900 and find it is 30, the negative square root would be: -30 This concept is especially important in various math problems, including solving quadratic equations and in complex number calculations. Negative square roots are simply the negative counterparts of positive square roots, indicating direction or sign rather than magnitude.

Nth Root Concept

The nth root concept generalizes the idea of square roots. The nth root of a number is a value that, when raised to the power of n, yields the original number. For example, the square root is a special case where n equals 2, represented as:\[x^2 = a\]Thus, the square root (or 2nd root) of a number a is often written as $ \sqrt{a} $. In the given problem, the task was to find the negative square root: a specific direction of a potential solution obtained from the square root calculation. Every non-zero number has n possible roots, including negative, positive, or complex varieties, based on the value of n.

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91影视

Find the indicated principal or negative \(n\)th root. $$-\sqrt{900}$$

Short Answer

Step by step solution

Identify the number

Find the square root

Apply the negative sign

Key Concepts

Square Root Calculation

Negative Numbers

Nth Root Concept

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