SOLUTION: I need help with this one. *Rationalize the denominator. Assume that no radicands were formed by raising negative numbers to even powers* Problem: Square root of 7a/32. Can anyo

Algebra ->  Algebra  -> Square-cubic-other-roots -> SOLUTION: I need help with this one. *Rationalize the denominator. Assume that no radicands were formed by raising negative numbers to even powers* Problem: Square root of 7a/32. Can anyo      Log On

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Question 538883: I need help with this one. *Rationalize the denominator. Assume that no radicands were formed by raising negative numbers to even powers* Problem: Square root of 7a/32. Can anyone help, I have been working on this problem forever. I need to show my work and I believe I have the correct answer, I am just struggling with the complete steps in between. I really want to understand how to work this problem and my text is not a lot of help with this. *Thanks =)*
Answer by Earlsdon(6287) About Me  (Show Source):
You can put this solution on YOUR website!
Rationalise the denominator:
sqrt%287a%2F32%29=sqrt%287a%29%2Fsqrt%2832%29
To "rationalise" the denominator means to remove the radical sign and this can be done here by multiplying the numerator and the denominator by sqrt%2832%29.
sqrt%287a%29%2Asqrt%2832%29%2F%28sqrt%2832%29%2Asqrt%2832%29%29 Substitute sqrt%2832%29%2Asqrt%2832%29+=+32
sqrt%287a%29%2Asqrt%2832%29%2F32 Perform the indicated multiplication in the numerator.
sqrt%2832%2A7a%29%2F32
sqrt%28224a%29%2F32 Rewrite 224+=+16%2A14
sqrt%2816%2A14a%29%2F32 Take the square root of 16 (that's 4) and move it outside the radical.
4%2Asqrt%2814a%29%2F32 Rewrite 32+=+4%2A8
4%2Asqrt%2814a%29%2F%284%2A8%29 Cancel the 4's
sqrt%2814a%29%2F8 or %281%2F8%29sqrt%2814a%29