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

Square Root of 1183

The square root of 1183 is expressed as √1183 in the radical form and as (1183)^½ or (1183)^0.5 in the exponent form. The square root of 1183 rounded up to 9 decimal places is 34.394767044. It is the positive solution of the equation x² = 1183. We can express the square root of 1183 in its lowest radical form as 13 √7.

Square Root of 1183: 34.39476704383968
Square Root of 1183 in exponential form: (1183)^½ or (1183)^0.5
Square Root of 1183 in radical form: √1183 or 13 √7

Square Root of 1183

1.	What is the Square Root of 1183?
2.	How to find the Square Root of 1183?
3.	Is the Square Root of 1183 Irrational?
4.	FAQs

What is the Square Root of 1183?

The square root of 1183, (or root 1183), is the number which when multiplied by itself gives the product as 1183. Therefore, the square root of 1183 = √1183 = 13 √7 = 34.39476704383968.

☛ Check: Square Root Calculator

How to Find Square Root of 1183?

Square Root of 1183 by Long Division Method

Value of √1183 by Long Division Method

Explanation:

Forming pairs: 11 and 83
Find a number Y (3) such that whose square is <= 11. Now divide 11 by 3 with quotient as 3.
Bring down the next pair 83, to the right of the remainder 2. The new dividend is now 283.
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 4) such that 6Z × Z <= 283. After finding Z, together 6 and Z (4) form a new divisor 64 for the new dividend 283.
Divide 283 by 64 with the quotient as 4, giving the remainder = 283 - 64 × 4 = 283 - 256 = 27.
Now, let's find the decimal places after the quotient 34.
Bring down 00 to the right of this remainder 27. The new dividend is now 2700.
Add the last digit of quotient to divisor i.e. 4 + 64 = 68. To the right of 68, find a digit Z (which is 3) such that 68Z × Z <= 2700. Together they form a new divisor (683) for the new dividend (2700).
Divide 2700 by 683 with the quotient as 3, giving the remainder = 2700 - 683 × 3 = 2700 - 2049 = 651.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1183.

Therefore, the square root of 1183 by long division method is 34.3 approx.

Is Square Root of 1183 Irrational?

The actual value of √1183 is undetermined. The value of √1183 up to 25 decimal places is 34.39476704383967767652100. Hence, the square root of 1183 is an irrational number.

☛ Also Check:

Square Root of 92 - √92 = 9.59166
Square Root of 120 - √120 = 10.95445
Square Root of 13 - √13 = 3.60555
Square Root of 240 - √240 = 15.49193
Square Root of 33 - √33 = 5.74456
Square Root of 320 - √320 = 17.88854
Square Root of 256 - √256 = 16

Square Root of 1183 Solved Examples

Example 1: Solve the equation x² − 1183 = 0

Solution:

x² - 1183 = 0 i.e. x² = 1183
x = ±√1183
Since the value of the square root of 1183 is 34.395,
⇒ x = +√1183 or -√1183 = 34.395 or -34.395.
Example 2: If the area of an equilateral triangle is 1183√3 in². Find the length of one of the sides of the triangle.

Solution:

Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a² = 1183√3 in²
⇒ a = ±√4732 in
Since length can't be negative,
⇒ a = √4732 = 2 √1183
We know that the square root of 1183 is 34.395.
⇒ a = 68.790 in
Example 3: If the area of a square is 1183 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 = 1183 in²
⇒ a = ±√1183 in
Since length can't be negative,
⇒ a = √1183 = 34.395 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 1183

What is the Value of the Square Root of 1183?

The square root of 1183 is 34.39476.

Why is the Square Root of 1183 an Irrational Number?

Upon prime factorizing 1183 i.e. 7¹ × 13², 7 is in odd power. Therefore, the square root of 1183 is irrational.

If the Square Root of 1183 is 34.395. Find the Value of the Square Root of 11.83.

Let us represent √11.83 in p/q form i.e. √(1183/100) = 11.83/10 = 3.439. Hence, the value of √11.83 = 3.439

What is the Square Root of -1183?

The square root of -1183 is an imaginary number. It can be written as √-1183 = √-1 × √1183 = i √1183 = 34.394i
where i = √-1 and it is called the imaginary unit.

What is the Square Root of 1183 in Simplest Radical Form?

We need to express 1183 as the product of its prime factors i.e. 1183 = 7 × 13 × 13. Therefore, √1183 = √7 × 13 × 13 = 13 √7. Thus, the square root of 1183 in the lowest radical form is 13 √7.

What is the Square of the Square Root of 1183?

The square of the square root of 1183 is the number 1183 itself i.e. (√1183)² = (1183)^2/2 = 1183.

Math worksheets and
visual curriculum