https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:rational-exp/v/basic-fractional-exponents 2021-06-30T17:32:34Z Intro to rational exponents What does it mean to take a number by a power which is a unit fraction? For example, what is the result of 3 raised to ½? Sal Khan video https://cdn.kastatic.org/googleusercontent/u1cMPoLA96VGGE3MKU_mWeqxgaGBivp-JTmMQNuqBzESWMHVn0o0nDNA4v8O2qRHpAFbdLwiwCk-pZaBYFlI53zC Intro to rational exponents What does it mean to take a number by a power which is a unit fraction? For example, what is the result of 3 raised to ½? https://cdn.kastatic.org/ka-youtube-converted/lZfXc4nHooo.mp4/lZfXc4nHooo.mp4 300 Radical expressions https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:rational-exp/v/rewriting-roots-as-rational-exponents 2022-10-06T23:23:50.639907812Z Rewriting roots as rational exponents Sal solves several problems about the equivalence of expressions with roots and rational exponents. For example, rewrite ⁶√(g⁵) as g^⅚. video https://cdn.kastatic.org/ka_thumbnails_cache/b128fb12-ed74-45d3-b989-7839975723d8_1280_720_base.png Rewriting roots as rational exponents Sal solves several problems about the equivalence of expressions with roots and rational exponents. For example, rewrite ⁶√(g⁵) as g^⅚. https://cdn.kastatic.org/ka-youtube-converted/gH4IsIEYof0.mp4/gH4IsIEYof0.mp4 259 Radical expressions https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:rational-exp/e/manipulating-fractional-exponents 2021-07-19T21:05:46.382456182Z Rational exponents challenge Choose equivalent forms of radical and exponential expressions. Tomer Gal exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:rational-exp/v/solving-for-a-fractional-exponent 2021-06-30T17:32:37Z Exponential equation with rational answer A worked example of rewriting a radical as an exponent. In this example, we solve for the unknown in 3ᵃ = ⁵√(3²). Sal Khan video https://cdn.kastatic.org/googleusercontent/tkloPRBhvOO0pvnhc4XYg8Ex__m9ToPeUGOUKHRTqmTgfenClr2k8pqUVqfdJCZvd4ERXBmLpY6wIlB-AVA8L8u8hg Exponential equation with rational answer A worked example of rewriting a radical as an exponent. In this example, we solve for the unknown in 3ᵃ = ⁵√(3²). https://cdn.kastatic.org/ka-youtube-converted/6OFwfxmhtE8.mp4/6OFwfxmhtE8.mp4 242 Radical expressions https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:exp-properties/v/simplifying-exponent-expression-with-division 2022-10-06T23:23:50.639907812Z Rewriting quotient of powers (rational exponents) Sal rewrites the expression m^(7/9) / m^(1/3) as a single exponential term m^(4/9). video https://cdn.kastatic.org/ka_thumbnails_cache/2d1ac82e-5efd-4bfa-b20f-abd460225103_1280_720_base.png Rewriting quotient of powers (rational exponents) Sal rewrites the expression m^(7/9) / m^(1/3) as a single exponential term m^(4/9). https://cdn.kastatic.org/ka-youtube-converted/0z-yIFzpunM.mp4/0z-yIFzpunM.mp4 151 Radical expressions https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:exp-properties/e/exponents_4 2025-07-25T20:49:26.361212747Z Properties of exponents intro (rational exponents) Rewrite exponential expressions (where the exponent can be a fraction) using the properties of exponents. Tomer Gal exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:exp/x2ec2f6f830c9fb89:exp-properties/e/rational-exp-prop-challenge 2026-03-05T15:50:38.258710261Z Properties of exponents (rational exponents) Rewrite some elaborate exponential expressions that involve fractional exponents and radicals. Tomer Gal exercise 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 Radical expressions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:simplifying-square-roots/e/simplifying_radicals 2021-07-08T21:56:40Z Simplify square roots For example, simplify √18 as 3√2. Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:simplifying-square-roots/v/simplifying-square-roots-comment-response 2020-12-28T16:56:57Z Simplifying square roots (variables) A worked example of simplifying radical with a variable in it. In this example, we simplify 3√(500x³). Sal Khan video https://cdn.kastatic.org/googleusercontent/xzFobbllMdm-T2s4VTJVNYosoACGSTyCsv1pGSNLHicw_jAyKdbemWQdkczlxZAdqbZfS6o1HPqNcScPguX0RG4FGA Simplifying square roots (variables) A worked example of simplifying radical with a variable in it. In this example, we simplify 3√(500x³). https://cdn.kastatic.org/ka-youtube-converted/qFFhdLlX220.mp4/qFFhdLlX220.mp4 256 Radical expressions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:simplifying-square-roots/e/multiplying_radicals 2025-06-26T20:46:37.500606524Z Simplify square roots (variables) Simplify square roots that contain variables in them, like √(8x³) Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:simplifying-square-roots/v/simplifying-square-root-expressions 2022-10-06T23:01:00.745424633Z Simplifying square-root expressions Worked examples of taking expressions with square roots and taking all of the perfect squares out of the square roots. For example, 2√(7x)⋅3√(14x²) can be written as 42x√(2x). video https://cdn.kastatic.org/ka_thumbnails_cache/65389dc8-7c65-4420-b13a-7cb11c9f7883_1280_720_base.png Simplifying square-root expressions Worked examples of taking expressions with square roots and taking all of the perfect squares out of the square roots. For example, 2√(7x)⋅3√(14x²) can be written as 42x√(2x). https://cdn.kastatic.org/ka-youtube-converted/3MijXB91DVo.mp4/3MijXB91DVo.mp4 510 Radical expressions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:simplifying-square-roots/e/adding_and_subtracting_radicals 2023-12-12T00:32:03.629852833Z Simplify square-root expressions Practice simplifying expressions with multiple radical terms. Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:simplifying-square-roots/a/simplifying-square-roots-review 2021-04-29T08:01:07Z Simplifying square roots review Learn how to rewrite square roots (and expressions containing them) so there's no perfect square within the square root. For example, rewrite √75 as 5⋅√3. article https://www.khanacademy.org/math/algebra-2-fl-best/x727ff003d4fc3b92:radical-functions-equations/x727ff003d4fc3b92:operations-with-irrational-numbers/e/rationalising-the-denominator-basic 2026-02-26T15:40:49.311158104Z Rationalising the denominator (basic) Rationalising the denominator (basic) anmol exercise https://www.khanacademy.org/math/algebra-2-fl-best/x727ff003d4fc3b92:radical-functions-equations/x727ff003d4fc3b92:operations-with-irrational-numbers/e/rationalising-the-denominator 2026-02-26T15:40:49.311158104Z Rationalising the denominator (advanced) Rationalising the denominator (advanced) anmol exercise 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 Radical expressions https://www.khanacademy.org/math/algebra-home/alg-exp-and-log/miscellaneous-radicals/v/adding-and-simplifying-radicals 2020-06-23T07:22:40Z Simplifying radical expressions (addition) A worked example of simplifying an expression that is a sum of several radicals. In this example, we simplify √(2x²)+4√8+3√(2x²)+√8. Sal Khan video https://cdn.kastatic.org/googleusercontent/HQ256M7LoD0RPMaWC5RRt7IN6Ali0tIVdBprzyRpzEjXJS0zmy55fygwDoYScaDT3HAShknytc3116w9PaQ43RXl0Q Simplifying radical expressions (addition) A worked example of simplifying an expression that is a sum of several radicals. In this example, we simplify √(2x²)+4√8+3√(2x²)+√8. https://cdn.kastatic.org/ka-youtube-converted/egNq4tSfi1I.mp4/egNq4tSfi1I.mp4 281 Radical expressions https://www.khanacademy.org/math/algebra-2-fl-best/x727ff003d4fc3b92:radical-functions-equations/x727ff003d4fc3b92:operations-with-irrational-numbers/e/adding-and-subtracting-irrational-numbers 2026-01-13T12:52:09.519257972Z Adding and subtracting irrational numbers Adding and subtracting irrational numbers anmol exercise https://www.khanacademy.org/math/algebra-2-fl-best/x727ff003d4fc3b92:radical-functions-equations/x727ff003d4fc3b92:operations-with-irrational-numbers/e/multiplying-irrational-numbers 2025-02-18T09:32:54.463014983Z Multiplying and dividing irrational numbers Multiplying irrational numbers anmol exercise 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 Radical expressions https://www.khanacademy.org/math/algebra-2-fl-best/x727ff003d4fc3b92:radical-functions-equations/x727ff003d4fc3b92:operations-with-irrational-numbers/e/multiplying-and-dividing-irrational-numbers 2026-02-26T15:40:49.311158104Z Multiplying irrational expressions Multiplying irrational expressions anmol exercise