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Chapter 10: Problem 2

In Exercises \(1-38,\) multiply as indicated. If possible, simplify any radical expressions that appear in the product. $$\sqrt{2}(x+\sqrt{7})$$

Short Answer

Expert verified
\(\sqrt{2}*x + \sqrt{14}\)

Step by step solution

01

Apply the Distributive Property

Multiply \(\sqrt{2}\) with each term in the parentheses (x and \(\sqrt{7}\)). This gives \(\sqrt{2}*x + \sqrt{2}*\sqrt{7}\).
02

Simplify the Radical Multiplication

Simplify \(\sqrt{2}*\sqrt{7}\) by multiplying the values under the radicals. The product of \(\sqrt{2}\) and \(\sqrt{7}\) is \(\sqrt{14}\). Hence, the expression becomes \(\sqrt{2}*x + \sqrt{14}\).
03

Final Expression

There are no like terms to combine, so the final simplified expression remains as \(\sqrt{2}*x + \sqrt{14}\).

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Most popular questions from this chapter

In Exercises \(65-74,\) simplify each radical expression and then rationalize the denominator. $$-\sqrt{\frac{75 a^{5}}{b^{3}}}$$

In Exercises \(39-64,\) rationalize each denominator. $$\sqrt[3]{\frac{3}{x y^{2}}}$$

Solve each equation. $$\sqrt[3]{x \sqrt{x}}=9$$

In Exercises \(129-132\), determine if each operation is performed correctly by graphing the function on each side of the equation with your graphing utility. Use the given viewing rectangle. The graphs should be the same. If they are not, correct the right side of the equation and then use your graphing utility to verify the correction. $$\begin{aligned} &(\sqrt{x}-1)(\sqrt{x}-1)=x+1\\\ &[0,5,1] \text { by }[-1,2,1] \end{aligned}$$

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