Difference between revisions of "Operations on Real Numbers"
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* <math>(\sqrt{a} +\sqrt{b})^2=a+2\sqrt{ab}+b</math> | * <math>(\sqrt{a} +\sqrt{b})^2=a+2\sqrt{ab}+b</math> | ||
== Examples == | |||
1.<math>(\sqrt{11} +\sqrt{7})(\sqrt{11} -\sqrt{b})</math> | 1.<math>(\sqrt{11} +\sqrt{7})(\sqrt{11} -\sqrt{b})</math> | ||
<math>11-7=4</math> | <math>11-7=4</math> | ||
2.<math>(\sqrt{3} +\sqrt{7})^2 </math> | 2.<math>(\sqrt{3} +\sqrt{7})^2 </math> | ||
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<math>10 +2(\sqrt{21}) </math> | <math>10 +2(\sqrt{21}) </math> | ||
3. <math>(5+\sqrt{7})(2 +\sqrt{5})</math> | |||
<math>10 + 5\sqrt{5}+2\sqrt{7}+\sqrt{35}</math> | |||
4.<math>(\sqrt{7} +\sqrt{5})(\sqrt{7} -\sqrt{5})</math> | |||
<math>(\sqrt{7})^2 - (\sqrt{5})^2</math> | |||
<math>7-5=2</math> |
Latest revision as of 22:05, 28 April 2024
Here we will be learning operations on Real Numbers.
Operations on Real Numbers Rules
- The sum or difference of a rational number and an irrational number is irrational.
- The product or quotient of a non-zero rational number with an irrational number is irrational number.
- When two irrational numbers are added, subtracted, multiplied or divided, the result may be a rational or an irrational number.
If a and b are positive real numbers, then we have,
Examples
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2.
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4.