Square Root of 289

The value of the square root of 289 is equal to 17. In radical form, it is represented as √289 = 17. 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. We will learn here both the methods one by one to simplify the root.

From the above value, we can define the square root of natural number 289, i.e. 17, is a value which when multiplied by itself gives the original number, i.e. 289 again.

Hence, 17 x 17 = 289 or 17² = 289

Simplification of Square Root of 289

Here, we will figure out the methods to find the square root of 289 using the prime factorisation and long division method.

By Prime Factorisation

As per prime factorisation, we need to find the prime factors present in a number. After finding the prime factors, we pair them in two, to take them out of the root. But this method is applicable only if the number is a perfect square.

Clearly, 289 is a perfect square, such as;

289 = 17 x 17

Therefore, if we take the square root on both the sides, we get;

√289 = √(17 x 17)

√289 = 17

By Long Division method

We can also find square root using long division method. This method is very useful not only to find the root of imperfect squares but also to find the root of large numbers. Let us find here the root of 289, using this method.

• Take the first digit i.e. 2 and leave the other two digits i.e. 89
• Now we can see 2 is near to square of 1. Therefore, taking 1 as divisor and quotient and 2 as dividend we get remainder as 1.
• Now, taking down the other two numbers, i.e. 89, next to the remainder 1 and adding 1 to the divisor to get our next divisor.
• Since the last digit is 9, then either the square of 3 or 7 can get the last digit as 9.
• Therefore, we will combine here 2 with 7 to get 27 x 7 equal to 189.
• Hence, the final answer is 17

Below is the solution for root of 289, based on the above steps.

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