Number system
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Rational numbers can be expressed as fractions of integers, and include all terminating and repeating decimals. Irrational numbers cannot be expressed as fractions and include numbers like √2 and √3. To prove that √3 is irrational, we assume it can be written as a/b where a and b are integers. Squaring both sides leads to a contradiction, since the left side is odd and right side is even. This proves that √3 cannot be written as a fraction of integers, so it is irrational.
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By Dr. Vinod Kumar KanvariaTypes of Herbal Cosmetics its standardization.
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Number system
- 1. number system Prepared by Golam Robbani Ahmed K.V.HPCL Jagiroad
- 2. Real Number:A real number may be either rational or irrational; either algebraic or transcenden tal; and either positive, negative, or zero
- 5. RATIONAL NUMBER All terminating decimal are rational number All non-terminating but repeating decimals are rational number All integer that can be expressed in the form of p/q(where p and q are integer and q ≠ 0 is called rational number.
- 6. Rational Number on Number line
- 7. Rational Number by successive magnification(ex: 2.65)
- 9. Irrational number on Number line
- 10. Geometrical representation of Real Number
- 11. To proof square root3 is an irrational number. Solution: To prove that this statement is true, let us assume that square root 3 is rational so that we may write Square root 3 = a/b Here a and b = any two integers. We must then show that no two such integers can be found. Squaring both side 3 = a²/b² 3b² = a² If b is odd then b² is odd. Similarly, if b is even, then b², a², and a are even. Since any choice of even values of a and b leads to a ratio a/b that can be reduced by canceling a common factor of 2. Suppose a² is odd than then b is odd that is a=2m+1 and b=2n+1 Putting the value of a and b in the above equation 3(4n² + 4n + 1) = 4m² + 4m + 1 6n² + 6n + 1 = 2(m² + m) The LHS of the above expression is odd and the RHS is even. That is a contradiction. That is square root 3 is irrational.