Square Root Using Tens and Ones Method
Square Root Using Tens and Ones Method
The square root of perfect squares up to four digits can be easily found by finding their ones and tens digits. To find out the square root of a given number, we have to follow these steps:
Step 1: Observe the ones digit of the perfect square and determine the digit in the ones place in the square root (using the table given below)
| Units digit of square: | 0 | 1 | 4 | 5 | 6 | 9 |
| Units digit of square root: | 0 | 1 or 9 | 2 or 8 | 5 | 4 or 6 | 3 or 7 |
If the perfect square has 1 or 4 or 5 or 9, then there are two possible ones digits.
Step 2: Strike out from the right the last two digits of the number. If nothing is left, we stop. The digit obtained in step 1 is the answer.
Step 3: Now consider the leftover number, and determine the largest 1-digit number whose square is less than or equal to this leftover number. This is the tens digit of the square root.
Note: If there are two possible answers, then the correct answer can be found by the actual multiplication.
Illustration: Find the square root of 6561 by finding its ones and tens digits.
Solution: Here, the ones digit of the given number is 1.So the ones digit of the square root is either 1 or 9.Now strike out from the right the last two digits of the number, we get the number 65.The square of 8,i.e.,64 is the largest square that is less than 65. As . Hence, the tens digit of the square root is 8.
So the square root of 6561 is either 81 or 89.
But , which is not equal to 6561.
Hence .
Illustration: Find the ten's digit in the square root of 625 by using the method of ones and tens digits.
Solution: Here, the ones digit of the given number is 5.So the ones digit of the square root is 5.Now strike out from the right the two digits of the number, we get the number 6.The square of 2,i.e.,4 is the largest square that is less than 6. As . Hence, the tens digit of the square root is 2.
Also the square root of 625 is 25.
Find the ten's digit in the square root of 3969 by using the method of ones and tens digits. | |||
| Right Option : A | |||
| View Explanation | |||
Find the ten's digit in the square root of 5625 by using the method of ones and tens digits. | |||
| Right Option : B | |||
| View Explanation | |||
Find the ten's digit in the square root of 2304 by using the method of ones and tens digits . | |||
| Right Option : C | |||
| View Explanation | |||
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