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Chapter 0: Problem 46

Rationalize the denominator. $$\frac{2}{\sqrt{10}}$$

Short Answer

Expert verified
The rationalized form of \( \frac{2}{\sqrt{10}} \) is \( \frac{\sqrt{10}}{5} \).

Step by step solution

01

Analyze the Fraction

The given fraction is \( \frac{2}{\sqrt{10}} \). The aim is to remove the square root from the denominator. The method used to do this is to multiply the fraction by a clever form of one, that doesn't change the value of the fraction, but helps to achieve our goal.
02

Form the Clever 1

The clever form of one in this case would be \( \frac{\sqrt{10}}{\sqrt{10}} \), since multiplying any number by its square root gives a rational number without a square root.
03

Multiply

Multiply the fraction \( \frac{2}{\sqrt{10}} \) by the clever form of 1, \( \frac{\sqrt{10}}{\sqrt{10}} \). We get \( \frac{2*\sqrt{10}}{\sqrt{10}*\sqrt{10}} \).
04

Simplify the Fraction

Simplify the fraction \( \frac{2*\sqrt{10}}{\sqrt{10}*\sqrt{10}} \) to get \( \frac{2*\sqrt{10}}{10} \).
05

Further Simplification

The fraction \( \frac{2*\sqrt{10}}{10} \) can be further simplified to \( \frac{2\sqrt{10}}{10} \). This is because 2 and 10 have a common factor of 2 that can be divided throughout. So, the final simplified fraction after rationalizing the denominator is \( \frac{\sqrt{10}}{5} \).

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. First factoring out the greatest common factor makes it easier for me to determine how to factor the remaining factor, assuming that it is not prime.

Simplify using properties of exponents. $$\left(7 x^{\frac{1}{3}}\right)\left(2 x^{\frac{1}{4}}\right)$$

Explain how to simplify \(\sqrt{10} \cdot \sqrt{5}\)

Exercises \(142-144\) will help you prepare for the material covered in the next section. Multiply: \(\quad\left(2 x^{3} y^{2}\right)\left(5 x^{4} y^{7}\right)\)

Evaluate each exponential expression in $$\frac{x^{14}}{x^{-7}}$$
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