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Square Root of 1089

The square root of 1089 is expressed as √1089 in the radical form and as (1089)^½ or (1089)^0.5 in the exponent form. The square root of 1089 is 33. It is the positive solution of the equation x² = 1089. The number 1089 is a perfect square.

Square Root of 1089: 33
Square Root of 1089 in exponential form: (1089)^½ or (1089)^0.5
Square Root of 1089 in radical form: √1089

Square Root of 1089

1.	What is the Square Root of 1089?
2.	How to find the Square Root of 1089?
3.	Is the Square Root of 1089 Rational?
4.	FAQs

What is the Square Root of 1089?

The square root of 1089, (or root 1089), is the number which when multiplied by itself gives the product as 1089. Therefore, the square root of 1089 = √1089 = 33.

☛ Check: Square Root Calculator

How to Find Square Root of 1089?

Square Root of 1089 by Long Division Method

Value of √1089 by Long Division Method

Explanation:

Forming pairs: 10 and 89
Find a number Y (3) such that whose square is <= 10. Now divide 10 by 3 with quotient as 3.
Bring down the next pair 89, to the right of the remainder 1. The new dividend is now 189.
Add the last digit of the quotient (3) to the divisor (3) i.e. 3 + 3 = 6. To the right of 6, find a digit Z (which is 3) such that 6Z × Z <= 189. After finding Z, together 6 and Z (3) form a new divisor 63 for the new dividend 189.
Divide 189 by 63 with the quotient as 3, giving the remainder = 189 - 63 × 3 = 189 - 189 = 0.
We stop the process since the remainder is now 0 and there are no more digits that can be brought down.

Therefore, the square root of 1089 by long division method is 33.

Is Square Root of 1089 Rational?

The value of √1089 is 33. Hence, the square root of 1089 is a rational number.

☛ Also Check:

Square Root of 56 - √56 = 7.48331
Square Root of 37 - √37 = 6.08276
Square Root of 106 - √106 = 10.29563
Square Root of 113 - √113 = 10.63015
Square Root of 89 - √89 = 9.43398
Square Root of 92 - √92 = 9.59166
Square Root of 16 - √16 = 4

Square Root of 1089 Solved Examples

Example 1: Solve the equation x² − 1089 = 0

Solution:

x² - 1089 = 0 i.e. x² = 1089
x = ±√1089
Since the value of the square root of 1089 is 33,
⇒ x = +√1089 or -√1089 = 33 or -33.
Example 2: If the surface area of a cube is 6534 in². Find the length of the side of the cube.

Solution:

Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a² = 6534 in²
⇒ a = ±√1089 in
Since length can't be negative,
⇒ a = √1089
We know that the square root of 1089 is 33.
⇒ a = 33 in
Example 3: If the area of a square is 1089 in². Find the length of the side of the square.

Solution:

Let 'a' be the length of the side of the square.
⇒ Area of the square = a² = 1089 in²
⇒ a = ±√1089 in
Since length can't be negative,
⇒ a = √1089 = 33 in

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FAQs on the Square Root of 1089

What is the Value of the Square Root of 1089?

The square root of 1089 is 33.

Why is the Square Root of 1089 a Rational Number?

Upon prime factorizing 1089 i.e. 3² × 11², we find that all the prime factors are in even power. This implies that the square root of 1089 is a positive integer. Therefore, the square root of 1089 is rational.

If the Square Root of 1089 is 33. Find the Value of the Square Root of 10.89.

Let us represent √10.89 in p/q form i.e. √(1089/100) = 10.89/10 = 3. Hence, the value of √10.89 = 3

What is the Square Root of -1089?

The square root of -1089 is an imaginary number. It can be written as √-1089 = √-1 × √1089 = i √1089 = 33i
where i = √-1 and it is called the imaginary unit.

What is the Square of the Square Root of 1089?

The square of the square root of 1089 is the number 1089 itself i.e. (√1089)² = (1089)^2/2 = 1089.

Evaluate 6 plus 4 square root 1089

The given expression is 6 + 4 √1089. We know that the square root of 1089 is 33. Therefore, 6 + 4 √1089 = 6 + 4 × 33 = 6 + 132 = 138

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