Question

Multiply or divide as indicated. $$\sqrt{5} \cdot \sqrt{-30}$$

   Multiply or divide as indicated.
$$\sqrt{5} \cdot \sqrt{-30}$$

Algebra for College Students

Algebra for College Students

Margaret L. Lial,… 9th Edition

Chapter 7, Problem 31

Instant Answer

Solved by Expert Vysakh M

02/21/2022

Step 1

Step 1: First, we rewrite the expression as follows: $$\sqrt{5} \cdot \sqrt{-30} = \sqrt{5} \cdot \sqrt{-1} \cdot \sqrt{30}$$ Show more…

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Multiply or divide as indicated. $$\sqrt{5} \cdot \sqrt{-30}$$

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Key Concepts

Properties of Radicals

This concept involves using the product rule for square roots, where, under proper conditions, multiplying two square roots can be expressed as the square root of the product of the numbers. This rule facilitates the simplification of expressions, but its applicability needs modification when dealing with negative values or complex numbers.

Complex Numbers

When encountering the square root of a negative number, it is necessary to extend the real number system to the complex number system. This extension introduces the concept of imaginary numbers and facilitates operations involving square roots of negative numbers.

Imaginary Unit

The imaginary unit, denoted by i, is defined by the property i² = -1. It is essential for expressing square roots of negative numbers, thereby enabling the computation and simplification of expressions that would otherwise be undefined in the real number system.

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