Question

सिद्ध कीजिए कि √2 एक अपरिमेय संख्या है।​

Answer 1

Question :-

Write the properties and uses of diamond.

Answer :-

Properties

1. Brilliant and pure diamond is the hardest natural substance.

2. The density of diamond is 3.5 g/cm³.

3. The melting point of diamond is 3500°C.

4. When diamond is heated at 800°C in the presence of Oxygen CO² is given away. In this process no other product besides CO² is formed.

5. Diamond does not dissolve in any solvent.

6. Acids/bases have no effect on diamond.

7. Diamond is a bad conductor of electricity and it does not have free electrons.

Uses

1. Diamonds are used in glass cutting and rock drilling machines.

2. Diamonds are used in ornaments.

3. Diamond knives are used in the eye surgery.

4. Diamond dust is used for polishing other diamonds.

5. Diamond is used to make windows giving protection from radiation in space and artificial satellites.

Answer 2

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Let's suppose √2 is a rational number. Then we can write it √2 = a/b where a, b are whole numbers, b not zero. We additionally assume that this a/b is simplified to lowest terms, since that can obviously be done with any fraction.

A proof that the square root of 2 is irrational.