17 17. Simplify square root of 289. Since the last digit is 9, then either the square of 3 or 7 can get the last digit as 9. The square root of two hundred and eighty-nine √289 = 17 How To Calculate Square Roots In mathematics, a square root of a number a is a number y such that y² = a, in other words, a number y whose square (the result of multiplying the number by itself, or y * y) is a. But the real question is what is a square and a square root? The square root of 289 is 17. This method is very useful not only to find the root of imperfect squares but also to find the root of large numbers. Square Root of 289. Finding Square Root Using Division Method. From the above value, we can define the square root of natural number 289, i.e. The steps to use the division method are given below. The square root of 9 will be 3 because it multiplies itself twice to give 9 i.e., 3 x 3 = 9. Pro Lite, Vedantu The perfect square root is not possible with numbers ending with 2, 3, 7, or 8. But on the other hand, 5 is the square root of 25. Finally, a new divisor will be obtained by taking the quotient twice and annexing with it a suitable digit which we can also take as the next digit of the quotient, selection should be in such a way that the product of new divisor and this digit must be equal to or just less than the new dividend. We call this the square root of 289 in radical form. One of the square root properties says that if a natural number is a square number, it will definitely be the sum of successive odd numbers starting from 1. Every pair and remaining one digit is known as a period. Consider the number as the divisor as well as the quotient. The nearest previous perfect square is 256 and the nearest next perfect square is 324 . We can find the square root of a number if we repeatedly subtract the successive odd numbers from the given square number, till it reaches zero. As per prime factorisation, we need to find the prime factors present in a number. The perfect square exists only with the perfect square. 2. So let us learn about them. Your email address will not be published. When we multiply any two positive numbers, we get a positive product as a result because both the positive numbers that we have multiplied have the same sign. There are two methods by which we can calculate square root without using a calculator: one is the prime factorisation and another is the long division method. The square root of 289 in mathematical form is written with the radical sign like this √289. Below is the solution for root of 289, based on the above steps. We will learn here both the methods one by one to simplify the root. This will become the new dividend. Think of the largest number you can think whose square will be equal to or maybe just less than the first period. This will become the new dividend. Let us find here the root of 289, using this method. √ 289 = q × q = q 2. 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