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28 Nov 2023

# Root Square of 289 – Simplifying, Prime Factorisation, and More

## Root Square of 289

17 is equal to the worth of the square root of 289. It is represented in radical form as 289 17.

There are two ways to calculate square roots without using a calculator: the prime factorization method and the long division method.

Here, we will learn both methods for simplifying the root, one by one.

Root square of 289, 289 = 17

From the initial value, we can deduce that the [square root] of 289, i.e., 17, is a number that, once multiplied by itself, produces the original number, i.e., 289.

Therefore, 17 x 17 equals 289, or 172 equals 289

## Simplifying Square Root 289

Here, we will determine in what way to calculate the square root of 289 using the prime factorization and long division.

### Through Prime Factorisation

• According to prime factorization, we must identify the number’s prime factors.
• After identifying the prime factors, we pair them to remove them from the root. However, this method only applies if the number is a perfect square.
• Obviously, 289 is a perfect square, for example: 289 = 17 x 17
• Taking the [square root] on both sides yields the following: 289 = (17 x 17) 289 = 17

### Long Division technique

The square root can also be found using the long division method. This method is beneficial for locating the square root of large numbers and the square roots of imperfect squares.

• Let’s calculate the [square root] of 289 using this method.
• Take the first digit, 2, and leave the remaining two digits, 89.

Now we can see that 2 is close to the square of 1. Consequently, using 1 as the divisor and quotient and 2 as the dividend yields a remainder of 1.

Now, record the remaining two digits, 89, next to the remainder, 1, and add 1 to the divisor to obtain the next divisor.

• Since the final digit is 9, either the square of 3 or 7 can yield 9 as the final digit.
• Therefore, we will multiply 2 by 7 to get 27 x 7, which equals 189.
• Therefore, the final response is 17
• [root square] of 289

The square of 17 yields the square number 289, which is a perfect square. The [square root] of 289 is, therefore, a rational number. This mini-lesson on finding the square root of 289 includes worked examples. Let’s determine the [square root] of 289.

• [Root Square] of 289: √289 = 17
• 2892 times 289 equals 83,521

## How Do You Calculate the Square Root of 289?

• The [square root] of 289 is the original number whose square is 289 times itself.
√289 = 17
• The answer obtained by squaring 17 is 289. Thus, 289 is a faultless fair.

### The Square Root of 289 Rational or Illogical

• However, a lucid amount can be either terminating or non-terminating, and its decimal component repeats a pattern.
• We observed that 289 = 17; seventeen is a whole number. It is straightforward to express in p/q form. 289 is, therefore, a rational number.