https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:irrational-numbers/x2f8bb11595b61c86:sums-and-products-of-rational-and-irrational-numbers/v/sum-and-product-of-rational-numbers 2020-12-28T16:56:56Z Proof: sum & product of two rationals is rational Sal proves that the sum, or the product, of any two rational numbers will always be a rational number. Sal Khan video https://cdn.kastatic.org/googleusercontent/tlGAB_Ca7KvNTDYokSylY2hxjhAs23qlMugitOwZIrJX_hiIDNWoYiWahGQH6I20_UwfQfFicj7GtwZZ5MHtJ0pztw Proof: sum & product of two rationals is rational Sal proves that the sum, or the product, of any two rational numbers will always be a rational number. https://cdn.kastatic.org/ka-youtube-converted/HKUJkMQsGkM.mp4/HKUJkMQsGkM.mp4 166 Sumas y productos de números racionales e irracionales https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:irrational-numbers/x2f8bb11595b61c86:sums-and-products-of-rational-and-irrational-numbers/v/proof-that-rational-times-irrational-is-irrational 2020-12-28T16:56:57Z Proof: product of rational & irrational is irrational The product of any rational number and any irrational number will always be an irrational number. This allows us to quickly conclude that 3π is irrational. Sal Khan video https://cdn.kastatic.org/googleusercontent/AidamtXLUX6FD3YyUttYNrHb3B3g8J-8EoXT4HvPJYeB339BToJxZrOgUQEk4lUpb6aEc4dKiWAg1YSyKA4sBrbNaA Proof: product of rational & irrational is irrational The product of any rational number and any irrational number will always be an irrational number. This allows us to quickly conclude that 3π is irrational. https://cdn.kastatic.org/ka-youtube-converted/KT32CsdEZEY.mp4/KT32CsdEZEY.mp4 195 Sumas y productos de números racionales e irracionales https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:irrational-numbers/x2f8bb11595b61c86:sums-and-products-of-rational-and-irrational-numbers/v/proof-that-sum-of-rational-and-irrational-is-irrational 2020-12-28T16:56:56Z Proof: sum of rational & irrational is irrational The sum of any rational number and any irrational number will always be an irrational number. This allows us to quickly conclude that ½+√2 is irrational. Sal Khan video https://cdn.kastatic.org/googleusercontent/wm98IU4tKB5alFmJxiq-hFMC_L7aHKjetjMP553R8MxgTd460p0FCOn_NbUv4nynnWjCgCoJZILzLNZ8syMLLK5-Fg Proof: sum of rational & irrational is irrational The sum of any rational number and any irrational number will always be an irrational number. This allows us to quickly conclude that ½+√2 is irrational. https://cdn.kastatic.org/ka-youtube-converted/pPM72fPwIjw.mp4/pPM72fPwIjw.mp4 204 Sumas y productos de números racionales e irracionales https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:irrational-numbers/x2f8bb11595b61c86:sums-and-products-of-rational-and-irrational-numbers/v/sums-and-products-of-irrational-numbers 2022-10-06T23:01:00.745424633Z Sums and products of irrational numbers The sum of two irrational numbers can be rational and it can be irrational. It depends on which irrational numbers we're talking about exactly. The same goes for products for two irrational numbers. This video covers this fact with various examples. video https://cdn.kastatic.org/ka_thumbnails_cache/99c2ca2a-cb87-4b56-99a7-1aba86c78e95_1280_720_base.png Sums and products of irrational numbers The sum of two irrational numbers can be rational and it can be irrational. It depends on which irrational numbers we're talking about exactly. The same goes for products for two irrational numbers. This video covers this fact with various examples. https://cdn.kastatic.org/ka-youtube-converted/16-GZWi66CI.mp4/16-GZWi66CI.mp4 357 Sumas y productos de números racionales e irracionales https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:irrational-numbers/x2f8bb11595b61c86:sums-and-products-of-rational-and-irrational-numbers/v/recognizing-rational-and-irrational-expressions-example 2021-06-02T12:43:24Z Worked example: rational vs. irrational expressions Sal shows how to determine whether the following expressions are rational or irrational: 9 + √(45), √(45)/ (3*√(5)), and 3*√(9). Sal Khan video https://cdn.kastatic.org/googleusercontent/KN85B5sBYmk11_CElBIk3JSY-6Mfazl6vxJPhpsC60AZEi2iu8PKln3HqDBPZkGQzEZJJ2e9v3KKbJtCTamE1GZV Worked example: rational vs. irrational expressions Sal shows how to determine whether the following expressions are rational or irrational: 9 + √(45), √(45)/ (3*√(5)), and 3*√(9). https://cdn.kastatic.org/ka-youtube-converted/hTJgK-wZMcE.mp4/hTJgK-wZMcE.mp4 156 Sumas y productos de números racionales e irracionales https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:irrational-numbers/x2f8bb11595b61c86:sums-and-products-of-rational-and-irrational-numbers/v/recognizing-rational-and-irrational-expressions-w-unknowns 2022-10-06T23:01:00.745424633Z Worked example: rational vs. irrational expressions (unknowns) Sal determines whether expressions with unknown rational/irrational numbers are rational or irrational. video https://cdn.kastatic.org/ka_thumbnails_cache/af3d1666-7b8d-4eb8-9559-025c71f52442_1280_720_base.png Worked example: rational vs. irrational expressions (unknowns) Sal determines whether expressions with unknown rational/irrational numbers are rational or irrational. https://cdn.kastatic.org/ka-youtube-converted/NC6HXlrH53Y.mp4/NC6HXlrH53Y.mp4 386 Sumas y productos de números racionales e irracionales https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:irrational-numbers/x2f8bb11595b61c86:sums-and-products-of-rational-and-irrational-numbers/e/recognizing-rational-and-irrational-expressions 2025-03-09T12:38:48.303569754Z Rational vs. irrational expressions Determine whether an expression that is the combination of two rational/irrational numbers is rational or irrational itself. Sid Patel exercise