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- Chapter 1- Rational and Irrational Numbers
- Chapter 2- Compound Interest [Without Using Formula
- Chapter 3- Compound Interest [Using Formula
- Chapter 4- Expansions
- Chapter 5- Factorisation
- Chapter 6- Simultaneous Equations
- Chapter 7- Indices [exponents]
- Chapter 8- Logarithms
- Chapter 9- Triangles [Congruency in Triangles]
- Chapter 10- Isosceles Triangle
- Chapter 11- Inequalities
- Chapter 12- Mid-Point and Its Converse
- Chapter 13- Pythagoras Theorem
- Chapter 14- Rectilinear Figures
- Chapter 15- Construction of Polygons
- Chapter 16- Area Theorems
- Chapter 17- Circles
- Chapter 18- Statistics
- Chapter 19- Mean and Median
- Chapter 20- Area and Perimeter of Plane Figures
- Chapter 21- Solids
- Chapter 22- Trigonometrical Ratios
- Chapter 23- Trigonometrical Ratios of Standard Angles
- Chapter 24- Solution Of Right Triangles
- Chapter 25- Complementary angles
- Chapter 26- Co-ordinate Geometry
- Chapter 27- Graphical Solution
- Chapter 28- Distance Formula

Show that:

(i) Negative of an irrational number is irrational.

(ii) The product of a non-zero rational number and an irrational number is an irrational number.

Answer:

(i) Let the irrational number be √2.

Considering the negative of √2, we get -√2

We know that -√2 is an irrational number.

Hence, negative of an irrational number is irrational.

(ii) Let the non-zero rational number be 3.

Let the irrational number be √5.

Then, according to the question,

3 × √5 = 3√5 = 3 × 2.2 = 6.6, which is irrational.

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