We have to find the square root of the no. & multiply it with -1 to find the answer. Also, the answer should be to the nearest integer & the nearest 10th. Using division method:
A) - √10
Write 10 as 10.00.. Pair the digits. Start from the decimal & move away from it. Hence, 1st pair would be 10, 2nd would be 00, & 3rd would be 00 and so onStart with the 1st pair, & find the no. whose square is ≤ first pair. So here, since first pair is 10, the no. whose square is just ≤ 10 is 3. Write 3 in the quotient and subtract 3² from 10 to get a remainder of 1We have reached the decimal in the dividend, so add a decimal in the quotient. Bring down the next pair to join with the remainder. The resulting no. is 100. Double the quotient (so 3 becomes 6) & use it to determine the divisor for 100. The divisor will be of the form 6x, & will be such that when it is multiplied with its unit digit then the product is ≤ 100 (i.e. 6x * x ≤ 100). So for x = 1, 61 *1 = 61, which is < 100. Append 1 to the quotient. The quotient now is 3.1. And subtract 31 (31*1) from 100 to find the remainder. The remainder is 39Bring down the next pair to join with the remainder. The resulting no. is 3900. Double the quotient (so 31 becomes 62) & use it to determine the divisor for 3900. The divisor will be of the form 62x, & will be such that when it is multiplied with its unit digit then the product is ≤ 3900 (i.e. 62x * x ≤ 3900). So for x = 6, 626 *6 = 3756. Append this 6 in the quotient. The quotient now is 3.16. And subtract 3756 from 3900 to find the remainder. The remainder is 144. We have square root of 10 up-till the 100th, so the answer is
- √10 = (-1) × √10 = (-1) × (3.16...) = -3.16..
Nearest 10th: - √10 = -3.2
Nearest integer: - √10 = -3
B) - √245
Pair the digits. Start from the decimal & move away from it. Hence, 1st pair would be 2, 2nd would be 45, & 3rd would be 00 & so onStart with the 1st pair, & find the no. whose square is ≤ the 1st pair. So that no. whose square is ≤ 2 is 1. Write 1 in the quotient and subtract 1² from 2 to get a remainder of 1. Bring down the next pair. The resulting no. is 145. Double the quotient (so 1 becomes 2) & use it to determine the divisor for 145. The divisor will be of the form 2x, & will be such that when it is multiplied with its unit digit then the product is ≤ 145. So for x = 5, 25 *5 = 125, which is < 145. Append the 5 in the quotient. The quotient is 15. And subtract 125 (15*5) from 145 to find the remainder. The remainder is 20We have reached the decimal in the dividend, so add a decimal in the quotient. Bring down the next pair. The resulting no. is 2000. Double the quotient (so 15 becomes 30) & use it to determine the divisor for 2000. The divisor will be of the form 30x, & will be such that when it is multiplied with its unit digit then the product is ≤ 2000. So for x = 6, 306 *6 = 1836. Append the 6 to the quotient. The quotient now is 15.6. And subtract 1836 from 2000 to find the remainder. The remainder is 164. Bring down the next pair. The resulting no. is 16400. Double the quotient (so 156 becomes 312) & use it to determine the divisor for 16400. The divisor will be of the form 312x, & will be such that when it is multiplied with its unit digit then the product is ≤ 16400. So for x = 5, 3125 *5 = 62604. Append this 5 in the quotient. The quotient now is 15.65. We have square root of 245 up-till the 100th, so the answer is
- √245 = (-1) × √245 = (-1) × (15.65...) = -15.65....
Nearest 10th: - √245 = -15.7
Nearest integer: - √245 = -16
C) - √52
Pair the digits. Start from the decimal & move away from it. Hence, 1st pair would be 52, 2nd would be 00, & so onStart with the 1st pair, & find the no. whose square is ≤ the 1st pair. So no. whose square is ≤ 52 is 7. Write 7 in the quotient & subtract 7² from 52 to get a remainder of 3We have reached the decimal in the dividend, so add a decimal in the quotient. Bring down the next pair, i.e. 00. The resulting no. is 300. Double the quotient (so 7 becomes 14) & use it to determine the divisor for 300. The divisor will be of the form 14x, & will be such that when it is multiplied with its unit digit the product is ≤ 300. So for x = 2, 142*2 = 284, which is < 300. Append the 2 in the quotient. The quotient now is 7.2. And subtract 284 (142*2) from 300 to find the remainder. The remainder is 16Bring down the next pair. The resulting no. is 1600. Double the quotient (so 72 becomes 144) & use it to determine the divisor for 1600. The divisor will be of the form 144x, & will be such that when it is multiplied with its unit digit then the product is ≤ 1600. So for x = 1, 1441*1 = 1441. Append the 1 to the quotient. The quotient now is 7.21. And subtract 1441 from 1600 to find the remainder. The remainder is 159. We have square root of 52 up-till the 100th, so the answer is
- √52 = (-1) × √52 = (-1) × (7.21...) = -7.21....
Nearest 10th: - √52 = -7.2
Nearest integer: - √52 = -7
