Find the square root of the following numbers by using their ones and tens digits
A)529
B)2601
C)1156
D)2209
Answers
Answer:
A) √529 = 23
B) √2601 = 51
C) √1156 = 34
D) √2209 = 47
Step-by-step explanation:
A) 529
At ones place the digit is 9. we know that 3² = 9 and 7² = 49. Therefore in the square root of 529, at ones place the number will be 3 or 7. Now if we leave the two digits from right we get 5. Again we have to check the squares. We know that 2² = 4 and 3² = 9 and 2² < 5 < 3². Therefore taking the perfect square closest to 5 we take the digit 2. Thus our square root is 23 (check 23 x 23 = 529).
B) 2601
At ones place the digit is 1. we know that 1² = 1 and 9² = 81, so 9 at the end will also give 1 at the end. Therefore in the square root of 2601, at ones place the number will be either 1 or 9. Now if we leave the two digits from right we get 26. Now we have to check the squares. We know that 5² = 25 and 6² = 36 and 5² < 26 < 6². Therefore taking the perfect square closest to 26 we take number 5. Thus our square root is should be either 51 or 59. If we multiply 51 x 51 we get 2601. Thus the square root of 2601 is 51.
C) 1156
At ones place the digit is 6. we know that 4² = 16 and 6² = 36, so 4 at the end will give 6 at ones place and 6 at the end will also give 6 at ones place. Therefore in the square root of 1156, at ones place the number will be either 4 or 6. Now if we leave the two digits from right we get 11. Now we have to check the squares. We know that 3² = 9 and 4² = 16 and 3² < 11 < 4². Therefore taking the perfect square closest to 11 we take number 3. Thus our square root is should be either 34 or 36. If we multiply 34 x 34 we get 1156. Thus the square root of 1156 is 34.
D) 2209
At ones place the digit is 9. we know that 3² = 9 and 7² = 49, so 3 at the end will give 9 at ones place and 7 at the end will also give 9 at ones place. Therefore in the square root of 2209, at ones place, the number will be either 3 or 7. Now if we leave the two digits from right we get 22. Now we have to check the squares. We know that 4² = 16 and 5² = 25 and 4² < 22 < 5². Therefore, taking the perfect square closest to 22 we take number 4. Thus our square root is should be either 43 or 49. If we multiply 49 x 49 we get 2209. Thus the square root of 2209 is 49.
Answer
a)529=23
b)2601=51
c)1156=34
d)2209=47
here is the answer