√2is irrational number. This can be proved using indirect proof
Answers
Answer:
Step 1: Write 2 as dividend in the division format. Add a point and then attach 6 to 8 zeros after the point. It is to get the appropriate number of decimal places in the decimal expansion of √2.
Step 2: Find the largest number whose square is less than or equal to the number 2. Take this number as the divisor and the quotient (1 in this case). Subtract and write the remainder.
Step 3: In the quotient, put a decimal point after 1. Bring down two zeroes to the right of the remainder. So, the new dividend is 100.
Step 4: Double the divisor and enter it as a new divisor with a blank on its right. Think about the greatest possible digit that can fill the blank which will also become the next digit in the quotient, such that when we multiply, the product should be either equal or less than the dividend. Subtract the numbers and write the remainder obtained.
Step 5: Then, we have to repeat the same process to get the desired number of decimal places. If required, we can add more zeros on the right of the original dividend, i.e, 2, in pairs.
