By Team Aakash Byju's
Square Root of 5=2.2360….
Square Root of Square root is found in 2 ways:
Prime factorization method
Can be done for perfect square root numbers
Long Division method
GCF of 5 and 30
5 = 5 30 = 2 x 3 x 5 GFC = 5
5 5 1
2 30 3 45 5 5 1
Can be done for all the numbers
Since 5 is not a perfect square number, calculating the value of √5 is not possible .Hence we need to use a long division method.
Write 5 as 5.000000000 i.e. 5. 00 00 00 00
Step 1
Now check for the largest number whose square is ≥ 5. ie 4 is perfect square of 2 and is the largest square number less or equal to 5
Step 2
Calculate the remainder and carry down two zero>Here the number formed is 100 .Let us consider this as x
Step 3
Step 4
Now add 2 in division 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 ≥ 100.
So when we multiply 42 by 2, we get 84, which is less than 100. Subtract it with 100 now to get the remainder as 16.
Step 5
Repeat steps 2, 3, 4 till the remainder is 0 or is repetitive.
Step 6
Quotient will be the square root