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Chapter 8: Problem 16

Multiply. In square roots, all variables represent positive values. SEE EXAMPLE 1. (OBJECTIVE 1) $$\sqrt{27} \sqrt{3}$$

Short Answer

Expert verified
The answer is 9.

Step by step solution

01

Multiply the Square Roots

Begin by multiplying the two square roots together. This results in \(\sqrt{27} \times \sqrt{3} = \sqrt{81}\)
02

Simplify the Result

The square root of 81 can be simplified, because 81 is a perfect square. The square root of 81 is 9.

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Key Concepts

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

Multiplying Square Roots
Understanding how to multiply square roots is a fundamental concept in algebra that enables the simplification of expressions involving radicals. When multiplying square roots, the key rule to remember is that \(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}\). This is because the operation of taking a square root and the operation of multiplication are

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Most popular questions from this chapter

Simplify each expression. All variables of square root expressions represent positive numbers. Assume no division by 0. $$\frac{3}{x^{2}} \sqrt{\frac{1}{81} x^{5} y z^{3}}$$

Simplify each expression. All variables of square root expressions represent positive numbers. Assume no division by 0. $$\frac{5}{6} \sqrt{180 a b^{2} c}$$

Explain the multiplication property of radicals.

Simplify each expression. All variables of square root expressions represent positive numbers. Assume no division by 0. $$-\frac{2}{5} \sqrt{80 m n^{2}}$$

Simplify. Assume that all variables in the radicand of an even root represent positive values. Assume no division by 0. Express each answer with positive exponents only. $$\left(4^{3 / 4} 3^{1 / 4}\right)^{4}$$
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