Alg 1
posted by Jane .
Simplifying Radicals
A gardener is mowing a 20ydby40 yd rectangular pasture using a diagonal pattern. He mows from one corner of the pasture to the cxorner diagonally opposite. What is the length of this pass with the mower? Give your answer in simplified form.
My answer choices are:
10(radical sign)20
20 (radical sign)2
400 (radical sign)5
20(radical sign)5
I don't know how to get the simplified radical. It sounds like I should be using the pythagorean Theorem, but that gives me 44.7  not one of the answers above. Thank you for your help.


Would you please show me how you arrived at the answer "D." I don't know how to set up the problem to get the answer. Thanks

√(20^2+40^2)
= √(400+1600)
= √2000
= √(400*5)
= √400√5
= 20√5
which, incidentally, is 44.7 :) 
You have the correct answer. Use your calculator for your choices and see which one gives you the same answer: both 1st and last answers give the same answer, but the last one is the correct answer. By the way, you are correct in using the Pythagorean Theorem, which gives hyp = sqrt(2000). To solve without a calculator, break down 2000 into factors that are square numbers:
sqrt(2000) = sqrt(100) * sqrt(20) =
10 * sqrt(20) (first answer, but not complete!!!
sqrt(100) * sqrt(20) =
10 * sqrt(4) * sqrt(5) =
10 * 2 * sqrt(5) = 20 * sqrt(5) 
Thanks you all so much!

Simplify. Write each answer in scientific notation.
1) (5.86 × 100
)(7.99 × 100
)