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Chapter 0: Problem 48

Rationalize the denominator. $$\frac{\sqrt{7}}{\sqrt{3}}$$

Short Answer

Expert verified
\(\frac{\sqrt{21}}{3}\)

Step by step solution

01

Identify the radicands

First, each number under the root is called a 'radicand'. So in the fraction \(\frac{\sqrt{7}}{\sqrt{3}}\), the radicands are \(7\) and \(3\).
02

Multiply by Conjugate

When rationalizing the denominator, multiply the numerator and denominator by the square root of the denominator's radicand. This would look like \(\frac{\sqrt{7}}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}}\). It is allowed to multiply like this since it is just equivalent to multiplying by 1, which does not change the fraction.
03

Simplify the Fraction

Simplify the fraction by applying the multiplication. Multiplying two square roots results to the radicand, hence, \(\sqrt{7}\times\sqrt{3}=\sqrt{21}\) and \(\sqrt{3}\times\sqrt{3}=\sqrt{9}=3\). This provides us the fraction \(\frac{\sqrt{21}}{3}\).

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