SOLUTION: I don't understand why simplifying 8/7sqrt2 becomes 4sqrt2/7; I thought it would become 8sqrt2/7. What am I not understanding about rationalizing denominators?

Algebra ->  Radicals -> SOLUTION: I don't understand why simplifying 8/7sqrt2 becomes 4sqrt2/7; I thought it would become 8sqrt2/7. What am I not understanding about rationalizing denominators?       Log On


   

Question 874139: I don't understand why simplifying 8/7sqrt2 becomes 4sqrt2/7; I thought it would become 8sqrt2/7.
What am I not understanding about rationalizing denominators?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To rationalize the denominator, we multiply top and bottom of the given fraction by sqrt%282%29. Doing so gives us...


8%2F%287%2Asqrt%282%29%29


%288%2Asqrt%282%29%29%2F%287%2Asqrt%282%29%2Asqrt%282%29%29


%288%2Asqrt%282%29%29%2F%287%2Asqrt%282%2A2%29%29


%288%2Asqrt%282%29%29%2F%287%2Asqrt%284%29%29


%288%2Asqrt%282%29%29%2F%287%2Asqrt%282%5E2%29%29


%288%2Asqrt%282%29%29%2F%287%2A2%29


%284%2A2%2Asqrt%282%29%29%2F%287%2A2%29


%284%2Ahighlight%282%29%2Asqrt%282%29%29%2F%287%2Ahighlight%282%29%29


%284%2Across%282%29%2Asqrt%282%29%29%2F%287%2Across%282%29%29


%284%2Asqrt%282%29%29%2F%287%29


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So, 8%2F%287%2Asqrt%282%29%29=%284%2Asqrt%282%29%29%2F%287%29