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Chapter 10: Problem 25

Evaluate or simplify each expression. (Assume \(x \geq 0 .)\) $$\sqrt{29} \sqrt{29}$$

Short Answer

Expert verified
29

Step by step solution

01

Identify the operation

Recognize that you need to simplify the expression \( \sqrt{29} \sqrt{29} \).
02

Apply the property of radicals

Use the property \( \sqrt{a} \sqrt{b} = \sqrt{a \times b} \). Here, \ a = 29 \ and \ b = 29 \.
03

Multiply the numbers under the radicals

Calculate the product of 29 and 29 to get \( 29 \times 29 = 841 \). Therefore, \( \sqrt{29} \sqrt{29} = \sqrt{841} \).
04

Simplify the square root

Since 841 is a perfect square, we have \( \sqrt{841} = 29 \).

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Key Concepts

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

radicals
Radicals are expressions that involve roots, such as square roots, cube roots, and so on. The symbol for a radical is the sqrt symbol, \(\sqrt{}\). It's often used to simplify expressions. For example, \(\sqrt{25}\) is 5 because 5 multiplied by itself gives 25. Radicals can be tricky, but they're essential in math to solve various equations and simplify expressions.
square roots
A square root is a type of radical. Finding the square root of a number means finding a value that, when multiplied by itself, gives the original number. For instance, \(\sqrt{16} = 4\) because \(4 \times 4 = 16\). Square roots are crucial in mathematics. They often show up in equations and help in simplifying numbers under a radical.
multiplication of radicals
Multiplying radicals involves a specific property: \(\sqrt{a} \sqrt{b} = \sqrt{a \times b}\). This property is handy when we need to simplify expressions. For example, consider \(\sqrt{29 \times 29}\), which simplifies to \(\sqrt{841}\). Since 841 is a perfect square, \(\sqrt{841} = 29\). This process shows how multiplication of radicals can simplify to a more manageable number.

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Most popular questions from this chapter

Describe the following statement in words: $$\sqrt{a} \sqrt{a}=a$$

Perform the indicated operations and simplify. $$\frac{3}{2 x}+\frac{5}{x+2}$$

In each of the following, perform the indicated operations and simplify as completely as possible. Assume all variables appearing under radical signs are non negative. $$\sqrt{2}+\sqrt{\frac{1}{2}}$$

In each of the following, perform the indicated operations and simplify as completely as possible. Assume all variables appearing under radical signs are non negative. $$\sqrt{18}+\sqrt{27}+\sqrt{45}$$

Rationalize the denominators and simplify. $$\frac{6}{3-\sqrt{7}}-\frac{21}{\sqrt{7}}$$
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