Ponder This Challenge - September 2000 - Simplify sqrt expression

Ponder This Challenge:

The August puzzle was rather tricky, for September we have a straightforward puzzle.

Simplify the following:
sqrt ( 3 - sqrt 5 ) + sqrt ( 4 + sqrt 7 ) + sqrt ( 6 - sqrt 35 )

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com

Solution

• Click here to view the solution

  sqrt (14)

  We can check that:
  sqrt ( 3 - sqrt 5 ) = sqrt (5/2) - sqrt(1/2),
  sqrt ( 4 + sqrt 7 ) = sqrt (7/2) + sqrt(1/2),
  sqrt (6 - sqrt 35 ) = sqrt ( 7/2) - sqrt (5/2),
  and their sum is
  2 sqrt ( 7/2) = sqrt (14).

  ---

  If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com

Solvers

• Ming Song (9.5.2000 @ 3:01 PM EDT)
• Mohit Sauhta (9.5.2000 @ 4:11 PM EDT)
• Muralidhar Seshadri (9.5.2000 @ 5:28 PM EDT)
• Lawrence T Hoff (9.5.2000 @ 5:53 PM EDT)
• Eben Stewart (9.5.2000 @ 8:22 PM EDT)
• Young Park (9.5.2000 @ 9:05 PM EDT)
• Amir Elad (9.6.2000 @ 7:09 AM EDT)
• Francis Golding (9.6.2000 @ 8:54 AM EDT)
• Gregoire Malandain (9.6.2000 @ 8:54 PM EDT)
• Dave Biggar (9.6.2000 @ 3:09 PM EDT)
• Ether Jones (9.6.2000 @ 3:30 PM EDT)
• Jim Morgan (9.6.2000 @ 6:40 PM EDT)
• Lenny Kneller (9.6.2000 @ 8:05 PM EDT)
• Ionel Santa (9.7.2000 @ 4:39 AM EDT)
• Samantha Levin (9.7.2000 @ 9:37 AM EDT)
• Olivier Miakinen (9.7.2000 @ 11:45 AM EDT)
• Jonathan A Wildstrom (9.7.2000 @ 12:51 PM EDT)
• Raju Krishnamoorthy (9.7.2000 @ 2:14 PM EDT)
• Bernard Widynski (9.7.2000 @ 3:10 PM EDT)
• Jessica Lang Jones (9.7.2000 @ 4:27 PM EDT)
• Guangwu Xu (9.7.2000 @ 4:46 PM EDT)
• Manikantan Srinivasan (9.7.2000 @ 4:59 PM EDT)
• Tao Lin (9.7.2000 @ 10:07 PM EDT)
• Shmuel Spiegel (9.7.2000 @ 10:34 PM EDT)
• Meredith Evans (9.8.2000 @ 9:27 AM EDT)
• Jacques Willekens (9.8.2000 @ 9:32 AM EDT)
• Scott Evans (9.8.2000 @ 1:01 PM EDT)
• Prithu Bharti Tiwari (9.8.2000 @ 3:35 AM EDT)
• Al Zimmermann (9.8.2000 @ 4:04 PM EDT)
• Alexis Megas (9.8.2000 @ 4:41 PM EDT)
• Philippe Fondanaiche (9.8.2000 @ 5:26 PM EDT)
• Arvind Narayanan (9.8.2000 @ 6:21 PM EDT)
• Roger Brooks (9.8.2000 @ 7:28 PM EDT)
• Achava Nakhash (9.9.2000 @ 12:25 PM EDT)
• Mihai Cioc (9.9.2000 @ 6:00 PM EDT)
• Stephan Voss (9.11.2000 @ 8:37 AM EDT)
• Howard Kaye (9.11.2000 @ 4:08 PM EDT)
• Andrew C Tong (9.11.2000 @ 4:48 PM EDT)
• Bill Daly (9.11.2000 @ 5:57 PM EDT)
• Donald Howes (9.12.2000 @ 1:46 AM EDT)
• Bruno DeNys (9.12.2000 @ 9:25 AM EDT)
• Prashanth Hande (9.12.2000 @ 6:09 PM EDT)
• HP Ravikiran (9.13.2000 @ 3:44 PM EDT)
• David J McKee (9.14.2000 @ 8:13 PM EDT)
• Tim Edmonds (9.15.2000 @ 8:36 AM EDT)
• Jarrus Mitchell (9.15.2000 @ 4:51 PM EDT)
• Walter Steets (9.16.2000 @ 2:36 PM EDT)
• Dmitri Asonov (9.17.2000 @ 11:14 AM EDT)
• Guenter Mair (9.17.2000 @ 1:11 PM EDT)
• Susan Schwartz Wildstrom (9.17.2000 @ 6:27 PM EDT)
• Jose F Martinez (9.18.2000 @ 1:00 AM EDT)
• Alexey Vorobyov (9.19.2000 @ 12:41 PM EDT)
• Peter Tran (9.19.2000 @ 3:42 PM EDT)
• Daniel Li (9.20.2000 @ 2:54 PM EDT)
• hyleeb (9.21.2000 @ 2:10 AM EDT)
• Christie Bolton (9.21.2000 @ 5:32 PM EDT)
• Rahul Gupta (9.22.2000 @ 6:40 PM EDT)
• Brad Long (9.27.2000 @ 3:39 AM EDT)
• Beimel Bernd (9.27.2000 @ 3:53 AM EDT)
• Rael Limbitco (9.27.2000 @ 5:08 PM EDT)
• Thomas Rohr (9.28.2000 @ 11:50 AM EDT)
• Edgar Romero (9.30.2000 @ 4:27 PM EDT)
• Chen Huang (10.01.2000 @ 1:00 AM EDT)
• Avi Shalav (10.01.2000 @ 12:59 PM EDT)