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Question

Evaluate the square root of 5


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Solution

We are going to use long division method to find square root of 5

The steps for finding the value of 5 is given below

Step 1:

The number 5 can be written as 5.00000000....

Step 2:

Take the number whose square is less than or equal to given number i.e 5.

So, 4 is the perfect square of number 2 and is below 5.

Step 3:

Write the number 2 in both divisor and quotient place, such that when 2 multiplied by 2 gives 4.

Subtract 4 from 5, we will get remainder 1.

Step 4:

Next carry down two zeros and write down after 1 and take the decimal point after 2 in the quotient.

Step 5: Now add 2 in divisor to make it 4. Take a number next to 4, such that when we multiply the combination with the same number, we get a number which is less than or equal to 100. Hence, we will take here 2, such that 42 multiplied by 2 gives 84, which is less than 100. Subtract it from 100 now to get the remainder. So, the remainder is 16.

Step 6: Now again write down two zero’s and repeat step 5 up to 3 places of decimals.

Step 7: Finally, you get the quotient value as 2.236 that will be non terminating non repeating decimal expansion.


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