To rationalize a radical in the denominator, multiply both the numerator and denominator by the same radical expression, which eliminates the radical from the denominator without changing the value of the fraction. For example, 2√3/7√2 becomes (2√3 × √2)/(7√2 × √2) = 2√6/7√4 = 2√6/14 = √6/7.
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Rationalizing Radicals Made EasyAdded:
Wait, are you still stuck with radicals in the denominator? Let me show you the fastest way to clean this up. We start with 2 root 3 over 7 root 2. Now, here's the trick. Multiply by root 2 over root 2. Why? Because it doesn't change the value, but it removes the radical from the bottom. Now, multiply straight across. On top, 2 root 3 * root 2 gives 2 root 6. On the bottom, 7 root 2 * root 2 gives 7 root 4. And root 4 is just 2.
So, now we have 2 root 6 over 7 * 2.
Simplify that and you get root 6 over 7.
Clean. Simple. Done. Stop overthinking radicals. Just multiply smart.
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