Examples: There are three digits in the square root of 546121, and four in the square root of 5774409.
For, marking off the digits from the right, we get in the first case 54,61,21, giving three digits in the square root, and in the second case 5,77,44,09, the odd digit giving the fourth in the square root.
The method of finding the square root of a given number depends on the form of the square of the sum of two numbers.
Explanation: The square root of 144 is 12. Let us see how we found it.
12 = 1 ten + 2 units.
122 is the same as (10 + 2)2.
Let us square (10 + 2), that is, multiply 10 + 2 by 10 + 2.
| 10 | + | 2 | ||
| 10 | + | 2 | ||
| 102 | + | (10 × 2) | ||
| + | (10 × 2) | + 22 | ||
| 102 | + | 2(10 × 2) | + 22 | |
| Then, 122 = | 102 | + | 2(10 × 2) | + 22 |
Rule.—The square of any number made up of tens and units is equal to the square of the tens, plus twice the product of the tens by the units, plus the square of the units.
Another Explanation: Find the square root of 45369.