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Chapter 0: Problem 47

Rationalize the denominator. $$\frac{\sqrt{2}}{\sqrt{5}}$$

Short Answer

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

Step by step solution

01

Identify the denominator to be rationalized.

Here, we have the denominator as \(\sqrt{5}\). This needs to be rationalized.
02

Rationalize the denominator.

To do this, we'll multiply both the numerator and denominator by the same square root term present in the denominator. So, multiply \(\frac{\sqrt{2}}{\sqrt{5}}\) by \(\frac{\sqrt{5}}{\sqrt{5}}\). Remember that \(\frac{\sqrt{5}}{\sqrt{5}}\) is 1, so we're not changing the value of the original fraction, just its appearance.
03

Perform the multiplication.

After the multiplication, the fraction becomes \(\frac{\sqrt{2}*\sqrt{5}}{\sqrt{5}*\sqrt{5}}\). Simplify this to \(\frac{\sqrt{10}}{5}\).

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Most popular questions from this chapter

How do you know if a number is written in scientific notation?

Will help you prepare for the material covered in the next section.Exercises \(144-146\) will help you prepare for the material covered in the next section. Factor the numerator and the denominator. Then simplify by dividing out the common factor in the numerator and the denominator. $$ \frac{x^{2}+6 x+5}{x^{2}-25} $$

Find the exact value of \(\sqrt{13+\sqrt{2}+\frac{7}{3+\sqrt{2}}}\) without the use of a calculator.

Describe what it means to rationalize a denominator. Use both \(\frac{1}{\sqrt{5}}\) and \(\frac{1}{5+\sqrt{5}}\) in your explanation.

Why is \(\left(-3 x^{2}\right)\left(2 x^{-5}\right)\) not simplified? What must be done to simplify the expression?
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