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Q&A #13682 |
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Hi Paul, I thought I'd share a different approach than what Suzanne has shared. I've used geoboards and the Pythagorean theorem to help students see sqrt(18) = 3sqrt(2) and sqrt(20) = 2sqrt(5). _ |_| Using the Pythagorean Thm, students can see that the length of the diagonal of a 1 by 1 square is sqrt(2). _ _ _ |_|_|_| Using the Pythagorean Thm, students can also see that the |_|_|_| length of the diagonal of a 3 by 3 square is sqrt(18). BUT |_|_|_| draw this diagonal on the adjacent picture, and hopefully, you can also see that this diagonal is exactly the same length as the diagonals of three 1 by 1 squares or 3sqrt(2). _ |_| Using the Pythagorean Thm, students can also see that the length of |_| the diagonal of this 2 by 1 rectangle is sqrt(5). _ _ |_|_| Using the Pythagorean Thm, students can see that the length of the |_|_| diagonal of this 4 by 2 rectangle is sqrt(20). BUT draw this |_|_| diagonal on the adjacent picture, and hopefully, you can also see |_|_| that this diagonal also has the same length as the diagonals of two 2 by 1 rectangles or 2sqrt(5). I can't use the geoboard to show that the sqrt(24) = 2sqrt(6) because I can't express either 6 or 24 as the sum of two perfect squares. (20 = 16+4; 5=4+1; 18=9+9) Hope this helps. -Jeanne, for the T2T service Thanks for visiting our on-line community. Visit Teacher2Teacher again at http://mathforum.org/t2t/
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