Find each root. 25k4m2\sqrt{$$25k^4$m^2$$} 25k4m2

Ch. R - Review of Basic Concepts

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Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 41

1장, 문제 41

Find each root. $\sqrt{25k^4m^2}$

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Identify the expression inside the square root: $\sqrt{25k^{4}m^{2}}$.

Recall the property of square roots that $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$, so rewrite the expression as $\sqrt{25} \cdot \sqrt{k^{4}} \cdot \sqrt{m^{2}}$.

Find the square root of each part separately: $\sqrt{25}$, $\sqrt{k^{4}}$, and $\sqrt{m^{2}}$.

Use the rule $\sqrt{x^{2}} = |x|$ to simplify the variable terms, so $\sqrt{k^{4}} = |k^{2}|$ and $\sqrt{m^{2}} = |m|$.

Combine all simplified parts to express the root as $5 \cdot |k^{2}| \cdot |m|$.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Square Root of a Product

The square root of a product can be expressed as the product of the square roots of each factor. For example, √(ab) = √a × √b. This property allows us to simplify complex expressions by breaking them into simpler parts.

Square Root of Variables with Exponents

When taking the square root of variables with exponents, divide the exponent by 2. For instance, √(x^n) = x^(n/2). This helps simplify expressions involving powers, especially when the exponent is even.

Simplifying Square Roots of Perfect Squares

A perfect square is a number or expression that is the square of an integer or variable expression. The square root of a perfect square is the base itself, such as √25 = 5 or √(k^4) = k^2, which simplifies the expression significantly.

Find each root. 25k4m2\(\sqrt{25k^4m^2}\) 25k4m2