Question

Make each denominator rational. In other words, rationalize the denominator.

Answer 1

☆Answer :

$\frac{3 + \sqrt{6} }{ \sqrt{6} } = ... \\ = \frac{3 + \sqrt{6} }{ \sqrt{6} } \times \frac{ \sqrt{6} }{ \sqrt{6} } = \frac{3 + ( \sqrt{6} \sqrt{6} ) }{6} \\ = \frac{3 + ( \sqrt{6} {}^{2}) }{6} = \frac{3 + 6}{6} \\ = \frac{9}{6} = \bold{1\frac{1}{2}}$

Answer 2

Answer:

$\frac{\sqrt6 + 2}{2}$

Step-by-step explanation:

Hello!

To rationalize the denominator, we want the denominator to be rid of any square root operations.

To do that we have to multiply the whole fraction by the value of the denominator, or multiply it by a Giant 1.

Rationalize:

• $\frac{3 + \sqrt6}{\sqrt6}$
• $\frac{3 + \sqrt 6}{\sqrt6} * \frac{\sqrt6}{\sqrt6}$
• $\frac{\sqrt6(3 + \sqrt6)}{\sqrt6 * \sqrt 6}$
• $\frac{3\sqrt6 + 6}{6}$

Simplify:

• $\frac{3(\sqrt6 + 2)}{3(2)}$
• $\frac{\sqrt6 + 2}{2}$

Final expression: $\frac{\sqrt6 + 2}{2}$

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Giant 1

A giant one is another term for a fraction that simplifies to 1. To simplify to

one, the fraction's numerator and denominator have to be the same. We

multiplied our expression by √6/√6, which doesn't change the value of the

original expression because we are technically multiplying by 1.