https://www.khanacademy.org/math/ncert-math-class-8-winter-bridge/x07a8c25cbfcc9660:week-1/x07a8c25cbfcc9660:untitled-212/v/classifying-numbers-indian-accent 2025-06-03T10:39:13.727334631Z Classifying numbers There are many categories we can use to classify numbers. Some of those categories are rational numbers, irrational numbers, integers, and whole numbers. Rational numbers are represented as a fraction of two integers, while irrational numbers cannot be represented as a fraction of two integers. Integers are positive and negative numbers that don’t involve fractions or decimals. Whole numbers are a subset of integers — they are non-negative integers. Kalakrit (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Classifying numbers There are many categories we can use to classify numbers. Some of those categories are rational numbers, irrational numbers, integers, and whole numbers. Rational numbers are represented as a fraction of two integers, while irrational numbers cannot be represented as a fraction of two integers. Integers are positive and negative numbers that don’t involve fractions or decimals. Whole numbers are a subset of integers — they are non-negative integers. https://cdn.kastatic.org/ka-youtube-converted/FCF0RUpXWIw.mp4/FCF0RUpXWIw.mp4 529 Real numbers https://www.khanacademy.org/math/revision-term-1-mh-math-class-8/x0c43044bb5624863:week-1/x0c43044bb5624863:rational-and-irrational-numbers/v/converting-a-fraction-to-a-repeating-decimal-india 2025-03-28T07:05:36.573142233Z Converting a fraction to a repeating decimal Converting a fraction to a repeating decimal (Indian Accent) Aakash Bagga video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Converting a fraction to a repeating decimal Converting a fraction to a repeating decimal (Indian Accent) https://cdn.kastatic.org/ka-youtube-converted/KtofePYDFz4.mp4/KtofePYDFz4.mp4 265 Real numbers https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:real-numbers/x06d55bfa213a79fd:operations-on-real-numbers/v/worked-example-rational-vs-irrational-expressions-india 2025-03-28T07:05:36.573142233Z Worked example: rational vs. irrational expressions Worked example: rational vs. irrational expressions (Indian Accent) Aakash Bagga video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Worked example: rational vs. irrational expressions Worked example: rational vs. irrational expressions (Indian Accent) https://cdn.kastatic.org/ka-youtube-converted/fMhzYAlrH2c.mp4/fMhzYAlrH2c.mp4 156 Real numbers https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-approximating-irrational-numbers/v/approximating-square-roots-2 2021-05-12T18:47:50Z Approximating square roots Learn how to find the approximate values of square roots. The examples used in this video are √32, √55, and √123. The technique used is to compare the squares of whole numbers to the number we're taking the square root of. video https://cdn.kastatic.org/googleusercontent/NmLYBMoaznVDSduejltf5ryy8CyjNviXgwJ2L6F-NB-hv3CqGMedj9-VGIDHbQgLCOWoehN2o_hS3WLUiAz7FeO0JA Approximating square roots Learn how to find the approximate values of square roots. The examples used in this video are √32, √55, and √123. The technique used is to compare the squares of whole numbers to the number we're taking the square root of. https://cdn.kastatic.org/ka-youtube-converted/Lh7NMBPFVZw.mp4/Lh7NMBPFVZw.mp4 288 Real numbers https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:simplifying-square-roots/v/simplifying-square-roots-1 2021-06-15T15:59:48Z Simplifying square roots Roots are nice, but we prefer dealing with regular numbers as much as possible. So, for example, instead of √4 we prefer dealing with 2. What about roots that aren't equal to an integer, like √20? Still, we can write 20 as 4⋅5 and then use known properties to write √(4⋅5) as √4⋅√5, which is 2√5. We *simplified* √20. Sal Khan video https://cdn.kastatic.org/googleusercontent/d7Em5BQ44iFafCzEh5eoNNi5HfjNVbnqGN0LzgQHMyGlxqjmkSLhHFv7rncwilYMp1OR_pY32IhYdpCTluMOUfrodQ Simplifying square roots Roots are nice, but we prefer dealing with regular numbers as much as possible. So, for example, instead of √4 we prefer dealing with 2. What about roots that aren't equal to an integer, like √20? Still, we can write 20 as 4⋅5 and then use known properties to write √(4⋅5) as √4⋅√5, which is 2√5. We *simplified* √20. https://cdn.kastatic.org/ka-youtube-converted/cw3mp8oNASk.mp4/cw3mp8oNASk.mp4 189 Real numbers https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:real-numbers/x06d55bfa213a79fd:operations-on-real-numbers/v/sums-and-products-of-irrational-numbers-india 2025-03-28T07:05:36.573142233Z Sums and products of irrational numbers Sums and products of irrational numbers (Indian Accent) Aakash Bagga video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Sums and products of irrational numbers Sums and products of irrational numbers (Indian Accent) https://cdn.kastatic.org/ka-youtube-converted/mMX6fWz0nvk.mp4/mMX6fWz0nvk.mp4 357 Real numbers https://www.khanacademy.org/math/algebra-basics/basic-alg-foundations/alg-basics-roots/v/simplifying-square-root-expressions-no-variables 2023-07-06T20:14:29.733919258Z Simplifying square-root expressions: no variables When square roots have the same value inside the radical, we can combine like terms. First we simplify the radical expressions by removing all factors that are perfect squares from inside the radicals. Then we can see whether we can combine terms or not. If there is only one term, there is nothing to combine. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Simplifying square-root expressions: no variables When square roots have the same value inside the radical, we can combine like terms. First we simplify the radical expressions by removing all factors that are perfect squares from inside the radicals. Then we can see whether we can combine terms or not. If there is only one term, there is nothing to combine. https://cdn.kastatic.org/ka-youtube-converted/74iuGIaBgRc.mp4/74iuGIaBgRc.mp4 380 Real numbers https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-negative-number-topic/cc-6th-absolute-value/v/absolute-value-of-integers 2023-06-30T02:13:42.781179102Z Absolute value examples The absolute value of a number represents its distance from zero on a number line, always resulting in a positive value. This concept is essential in mathematics, as it helps to simplify calculations and understand the magnitude of numbers, regardless of their positive or negative sign. Examples include finding the absolute values of 5, -10, and -12. Sal Khan video https://cdn.kastatic.org/googleusercontent/0CiS0-HzLVFZCI-0u5H2CN_d6PxpPUNUr9o3VXnhJKRRLiZ4q94ukeS0STT3FR0jCDKlU631lt4hdXclkfJDd_LRsA Absolute value examples The absolute value of a number represents its distance from zero on a number line, always resulting in a positive value. This concept is essential in mathematics, as it helps to simplify calculations and understand the magnitude of numbers, regardless of their positive or negative sign. Examples include finding the absolute values of 5, -10, and -12. https://cdn.kastatic.org/ka-youtube-converted/r6hS_8nm1jM.mp4/r6hS_8nm1jM.mp4 142 Real numbers https://www.khanacademy.org/math/revision-mh-math-class-9/x6ee29cf0de77cbed:week-1/x6ee29cf0de77cbed:real-numbers/e/revision-real-numbers-mh-class-9 2026-02-03T09:22:16.808346173Z Revision real numbers MH class 9 . Khan Academy exercise