Square Root of 289

Square root of 289 is ±17. Here, 17 is the number which when multiplied by itself will give the product equal to 289. In radical form, it is written as √289. To find the square root of 289, we have to use the methods like long division method and the Prime Factorisation method.

In this article, we will learn about square root of 289 and the methods to determine the root value of 289.

What is Square Root of 289?

Square root of 289 is represented as √289. It is the value that is squared or multiplied by itself to obtain the original number. The opposite of squaring a number is to obtain its square root. Therefore, In this case, the square root of 289 is 17. The value of square root of 289 in different forms is given below:

• Integer form: ±17
• Radical form: √289
• Exponent form: (289)^1/2

Square Root Calculator

Try out the following calculator to find the square root of 289

How to Calculate Square Root of 289?

To find the square root of 289, we can use the methods that are given below:

• Long Division Method
• Prime Factorization Method

Square Root of 289 by Long Division Method

The following steps must be followed to determine the square root of 289:

• Step 1: Start with the number 289 and begin grouping the numbers into pairs from right to left.
• Step 2: Choose a perfect square less than or equal to 2. Divide it and write the quotient which is 1 and the remainder is 1.
• Step 3: Write down the next pair to the right side of the remainder(which is 89).
• Step 4: Now add the divisor with the quotient which is 1 + 1 = 2, and write down by leaving some space on the right side.
• Step 5: Add a digit at the left of 2 in the divisor i.e. at the unit place and also place the same digit in the quotient such that the product is near or equal to 189.
• Step 6: Add 4 in the divisor using step 5 hence, the new dividend will be 27 × 7 = 189. The remainder becomes 0, hence 17 is the square root of 289.

Below is the pictorial representation of this method.

Learn, Square Root by Long Division Method

Square Root of 289 by Prime Factorization Method

To find square root of 289 by prime factorization method, we first prime factorize 289 and then make pairs of integers to get the square root.

So, let’s express the √289 in the following steps;

289 = 17 x 17or 289 = 17²

√289= √(17 x 17) (Taking roots on both sides)
= 17

√289 = 17

Therefore, square root of 289 is equal to 17.

Is Square Root of 289 Rational or Irrational?

Square Root of 289 is a rational number. A rational number is simply the ratio of two integers i.e. any number which can be written in the form of p/q is a rational number. In case of 289, the square root of 289:

√289 = 17

So, the square root of 289 shows us that it is an integer. Therefore, Square root of 289 is a rational number.

Solved Examples

Example 1: Simplify the square root of 289.

Solution:

• First, we will find out the prime factors of 289.
  289 = 17 × 17
• After that, combine prime factors into pairs:
  289 = 17²
• Then take square root on both sides
  √289 = √17²
• At last, simplify it
  √289= 17

Therefore, the square root of 289 can be simplified to 17.

Example 2: Solve the equation: √x = 289.

Solution:

The procedures below can be used to solve the equation √x = 289, where x is a real number:

• First, square both sides of the equation.
  (√x)² = (289)²
• After simplifying both sides we get;
  x = 83521

So, The equation √x = 289 has a value of x = 83521.

Example 3: If one side of a rectangle is √289 cm and the other side is 10 cm, find the area.

Solution:

Area of the rectangle when one side is √289 cm
Other side is 10 cm

Area = Length × Width (Length = √289 cm,Width = 10 cm)
Area = (√289 cm) × (10 cm)
Area = 17 × 10 = 170 cm²

Therefore,area of the rectangle is 170 cm².

Square Root of 289 – FAQs

What is Square Root of 289?

Square root of 289 is ±17.

Is √289 a Rational Number?

Yes, √289 is a rational number as its value is ±17 which is an integer, hence a rational number.

Is 289 a Prime Number?

No, 289 is not a prime number because it has more than two factors.

What is Square Root of 289 in Radical Form?

The square root of 289 in radical form is √289.

Is 289 a perfect square?

Yes, 289 is a perfect square.

Is -17 a square root of 289?

Yes, -17 is a square root of 289 because when -17 is multiplied by itself it returns back 289.

What is Cube Root of 289?

The cube root of 289 in approximate value is 6.611.