A day full of math games & activities. Find one near you.

Square Root of 1069

The square root of 1069 is expressed as √1069 in the radical form and as (1069)^½ or (1069)^0.5 in the exponent form. The square root of 1069 rounded up to 5 decimal places is 32.69557. It is the positive solution of the equation x² = 1069.

Square Root of 1069: 32.69556544854363
Square Root of 1069 in exponential form: (1069)^½ or (1069)^0.5
Square Root of 1069 in radical form: √1069

Square Root of 1069

1.	What is the Square Root of 1069?
2.	How to find the Square Root of 1069?
3.	Is the Square Root of 1069 Irrational?
4.	FAQs

What is the Square Root of 1069?

The square root of 1069, (or root 1069), is the number which when multiplied by itself gives the product as 1069. Therefore, the square root of 1069 = √1069 = 32.69556544854363.

☛ Check: Square Root Calculator

How to Find Square Root of 1069?

Square Root of 1069 by Long Division Method

Value of √1069 by Long Division Method

Explanation:

Forming pairs: 10 and 69
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 69, to the right of the remainder 1. The new dividend is now 169.
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 2) such that 6Z × Z <= 169. After finding Z, together 6 and Z (2) form a new divisor 62 for the new dividend 169.
Divide 169 by 62 with the quotient as 2, giving the remainder = 169 - 62 × 2 = 169 - 124 = 45.
Now, let's find the decimal places after the quotient 32.
Bring down 00 to the right of this remainder 45. The new dividend is now 4500.
Add the last digit of quotient to divisor i.e. 2 + 62 = 64. To the right of 64, find a digit Z (which is 6) such that 64Z × Z <= 4500. Together they form a new divisor (646) for the new dividend (4500).
Divide 4500 by 646 with the quotient as 6, giving the remainder = 4500 - 646 × 6 = 4500 - 3876 = 624.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1069.

Therefore, the square root of 1069 by long division method is 32.6 approximately.

Is Square Root of 1069 Irrational?

The actual value of √1069 is undetermined. The value of √1069 up to 25 decimal places is 32.69556544854362967589966. Hence, the square root of 1069 is an irrational number.

☛ Also Check:

Square Root of 14 - √14 = 3.74166
Square Root of 100 - √100 = 10
Square Root of 80 - √80 = 8.94427
Square Root of 48 - √48 = 6.92820
Square Root of 49 - √49 = 7
Square Root of 27 - √27 = 5.19615
Square Root of 41 - √41 = 6.40312

Square Root of 1069 Solved Examples

Example 1: Solve the equation x² − 1069 = 0

Solution:

x² - 1069 = 0 i.e. x² = 1069
x = ±√1069
Since the value of the square root of 1069 is 32.696,
⇒ x = +√1069 or -√1069 = 32.696 or -32.696.
Example 2: If the surface area of a cube is 6414 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 = 6414 in²
⇒ a = ±√1069 in
Since length can't be negative,
⇒ a = √1069
We know that the square root of 1069 is 32.696.
⇒ a = 32.696 in
Example 3: If the surface area of a sphere is 4276π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 4276π in²
⇒ r = ±√1069 in
Since radius can't be negative,
⇒ r = √1069
The square root of 1069 is 32.696.
⇒ r = 32.696 in

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on the Square Root of 1069

What is the Value of the Square Root of 1069?

The square root of 1069 is 32.69556.

Why is the Square Root of 1069 an Irrational Number?

The number 1069 is prime. This implies that the number 1069 is pairless and is not in the power of 2. Therefore, the square root of 1069 is irrational.

What is the Square Root of -1069?

The square root of -1069 is an imaginary number. It can be written as √-1069 = √-1 × √1069 = i √1069 = 32.695i
where i = √-1 and it is called the imaginary unit.

Evaluate 8 plus 15 square root 1069

The given expression is 8 + 15 √1069. We know that the square root of 1069 is 32.696. Therefore, 8 + 15 √1069 = 8 + 15 × 32.696 = 8 + 490.433 = 498.433

What is the Square of the Square Root of 1069?

The square of the square root of 1069 is the number 1069 itself i.e. (√1069)² = (1069)^2/2 = 1069.

If the Square Root of 1069 is 32.696. Find the Value of the Square Root of 10.69.

Let us represent √10.69 in p/q form i.e. √(1069/100) = 10.69/10 = 3.270. Hence, the value of √10.69 = 3.270

Math worksheets and
visual curriculum