Question
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Answer
The simplified form is \( \frac{\sqrt{2}}{2} \).
Solution
Calculate or simplify the expression \( \frac{\sqrt{3}}{\sqrt{6}} \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{\sqrt{3}}{\sqrt{6}}\)
- step1: Rewrite the expression:
\(\frac{\sqrt{3}}{\sqrt{3}\times \sqrt{2}}\)
- step2: Reduce the fraction:
\(\frac{1}{\sqrt{2}}\)
- step3: Multiply by the Conjugate:
\(\frac{\sqrt{2}}{\sqrt{2}\times \sqrt{2}}\)
- step4: Multiply the numbers:
\(\frac{\sqrt{2}}{2}\)
The simplified form of \( \frac{\sqrt{3}}{\sqrt{6}} \) is \( \frac{\sqrt{2}}{2} \).
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Simplify this solution Bonus Knowledge
To simplify \( \frac{\sqrt{3}}{\sqrt{6}} \), you can multiply the numerator and the denominator by \( \sqrt{6} \) to rationalize it. This gives you \( \frac{\sqrt{3} \cdot \sqrt{6}}{6} = \frac{\sqrt{18}}{6} \). Since \( \sqrt{18} = 3\sqrt{2} \), you can break it down further to arrive at \( \frac{3\sqrt{2}}{6} = \frac{\sqrt{2}}{2} \). Voilà! Now you have a much neater expression, \( \frac{\sqrt{2}}{2} \), which pops up in various areas of math, especially in trigonometry when dealing with angles in a unit circle, making it a handy tool in your math toolkit!
