SOLUTION: find the ara of the rectangle top is square root of 3+square root of 5 right side is the same

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Question 83446: find the ara of the rectangle
top is square root of 3+square root of 5
right side is the same
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Area of a rectangle is L*W. It seems that the length and width are the same: sqrt%283%29+%2B+sqrt%285%29+

AREA = %28sqrt%283%29+%2B+sqrt%285%29%29%5E2+
A= +%28sqrt%283%29+%2B+sqrt%285%29%29%2A%28sqrt%283%29+%2B+sqrt%285%29+%29+

You must multiply this out, like a FOIL problem:
A= +%28sqrt%283%29+%2B+sqrt%285%29%29%2A%28sqrt%283%29+%2B+sqrt%285%29+%29+
A= +sqrt%289%29+%2B+sqrt%2815%29%2Bsqrt%2815%29+%2B+sqrt%2825%29++

Notice that the middle terms are like terms, and they combine 1%2Asqrt%2815%29%2B1%2Asqrt%2815%29+=+2%2Asqrt%2815%29+
A= +3+%2B+2%2Asqrt%2815%29+%2B+5++
A = 8+%2B+2%2Asqrt%2815%29+

For more help with products of radicals like this one, see my Lesson Plans in algebra.com, or go to my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com, then look for "MATH IN LIVING COLOR" then look for Basic Algebra, Chapter 5. The entire chapter is on Square Roots (and more!),

R^2 at SCC