Question

find the square root of 5.25 correct upto 4 places of decimal​

Answer 1

Answer:

2.2912878

Step-by-step explanation:

if we do squaring of 2.2912878 then it will become 5.25

Answer 2

Group the digits into pairs (For digits to the left of the decimal point, pair them from right to left. For digits after decimal point, pair them from left to right).

Thus we have, $\blue{05}.\red{25}$

Perform division as per steps shown below:

⎇ Find the largest number whose square is less than or equal to the number in the

leftmost group

$( {2}^{2} < 5 < {3}^{3} ).$

Take this number as the divisor and the quotient with the number in the leftmost group as the dividend (05). Divide and get the remainder (1 in this case).

➲ (1st image is in f1st ATTACHMENT)

⎇ Put the decimal point.

⎇ Bring down the next pair 25. Add the divisor with the quotient and enter it with a blank on its right. Guess a largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. In this case 42 × 2 = 84, so we choose the new digit as 2. Get the remainder.

➲ (2nd image in 2nd ATTACHMENT)

⎇ Remember: A decimal number, say3 can be written as 3.0, 3.00 and so on. Bring down the next pair 00. Add the divisor with the quotient and enter it with a blank on its right. Guess a largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. In this case 449 × 9 = 4041, so we choose the new digit as 9. Get the remainder.

➲ (3rd image in 3rd attachment)

⎇ Remember: A decimal number, say3 can be written as 3.0, 3.00 and so on. Bring down the next pair 00. Add the divisor with the quotient and enter it with a blank on its right. Guess a largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. In this case 4581 × 1 = 4581, so we choose the new digit as 1. Get the remainder.

➲ (4th image in 4th ATTACHMENT)

⎇ End of long division (upto 3 decimal places).

of long division (upto 3 decimal places).√5.25 = 2.291