ICSE Class 9 Answered

sir, please explain irrational numbers and surds in simple words ???....

Asked by Sumanglam | 06 Apr, 2016, 08:27: AM

Expert Answer

Irrational space number colon space Consider space the space number space 0.202002000200002..... space Observe space that space there space are space either space 2 apostrophe straight s space or space 0 apostrophe straight s space and space the space 2 apostrophe straight s space are space separated space respectively space by space one space zero comma space then space two space zeros comma space then space three space zeros space and space so space on. space Clearly space the space number space of space zeros space separating space successive space 2 apostrophe straight s space goes space on space increasing space successively space by space one. space So space we space can space go space on space writing space this space decimal space endlessly. space That space means space that space the space decimal space representation space is space non minus terminating. space Further space observe space that space no space group space of space digits space repeats. space So comma space the space decimal space representation space of space the space number space is space non minus repeating. space Such space straight a space number space cannot space be space written space in space the space form space straight p over straight q space where space straight p comma space straight q space are space integers space and space straight q space is space not space equal space to space 0. So comma space straight a space number space is space an space irrational space number space if space it space has space straight a space non minus terminating space and space non minus repeating space decimal space representation. Surds colon Consider space the space numbers space square root of 2 space left parenthesis that space is space square space root space of space 2 right parenthesis space and space square root of 4 space left parenthesis that space is space square space root space of space 4 right parenthesis. The space number square root of 2 space cannot space be space simplified space further space to space get space its space exact space value comma space but space the space number space square root of 4 space can space be space simplified space further space to space 2. Such space numbers space which space are space left space in space root space form space left parenthesis square root of blank end root right parenthesis space to space express space its space exact space value space and space which space cannot space be space simplified space to space remove space the space root comma space it space called space straight a space surd. So comma space space square root of 2 space is space straight a space surd comma space while space space square root of 4 space is space not space straight a space surd. space space square root of 2 equals 1.4142135........ So comma space surds space have space straight a space decimal space which space goes space on space endlessly space without space repeating space and space thus space are space Irrational space numbers.

Answered by Rebecca Fernandes | 06 Apr, 2016, 09:00: AM

ICSE Class 9 Answered

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ICSE Class 9 Answered

Application Videos

Irrational Numbers - 1

Irrational Numbers - 2

Irrational Numbers

Rational and Irrational Numbers

Concept Videos

Irrational Numbers

Irrational Numbers

Irrational Numbers ...

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