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Square Root of 1331

The square root of 1331 is expressed as √1331 in the radical form and as (1331)^½ or (1331)^0.5 in the exponent form. The square root of 1331 rounded up to 9 decimal places is 36.482872694. It is the positive solution of the equation x² = 1331. We can express the square root of 1331 in its lowest radical form as 11 √11.

Square Root of 1331: 36.4828726939094
Square Root of 1331 in exponential form: (1331)^½ or (1331)^0.5
Square Root of 1331 in radical form: √1331 or 11 √11

Square Root of 1331

1.	What is the Square Root of 1331?
2.	How to find the Square Root of 1331?
3.	Is the Square Root of 1331 Irrational?
4.	FAQs

What is the Square Root of 1331?

The square root of 1331, (or root 1331), is the number which when multiplied by itself gives the product as 1331. Therefore, the square root of 1331 = √1331 = 11 √11 = 36.4828726939094.

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How to Find Square Root of 1331?

Square Root of 1331 by Long Division Method

Value of √1331 by Long Division Method

Explanation:

Forming pairs: 13 and 31
Find a number Y (3) such that whose square is <= 13. Now divide 13 by 3 with quotient as 3.
Bring down the next pair 31, to the right of the remainder 4. The new dividend is now 431.
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 6) such that 6Z × Z <= 431. After finding Z, together 6 and Z (6) form a new divisor 66 for the new dividend 431.
Divide 431 by 66 with the quotient as 6, giving the remainder = 431 - 66 × 6 = 431 - 396 = 35.
Now, let's find the decimal places after the quotient 36.
Bring down 00 to the right of this remainder 35. The new dividend is now 3500.
Add the last digit of quotient to divisor i.e. 6 + 66 = 72. To the right of 72, find a digit Z (which is 4) such that 72Z × Z <= 3500. Together they form a new divisor (724) for the new dividend (3500).
Divide 3500 by 724 with the quotient as 4, giving the remainder = 3500 - 724 × 4 = 3500 - 2896 = 604.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1331.

Therefore, the square root of 1331 by long division method is 36.4 approximately.

Is Square Root of 1331 Irrational?

The actual value of √1331 is undetermined. The value of √1331 up to 25 decimal places is 36.48287269390939834026426. Hence, the square root of 1331 is an irrational number.

☛ Also Check:

Square Root of 15 - √15 = 3.87298
Square Root of 41 - √41 = 6.40312
Square Root of 56 - √56 = 7.48331
Square Root of 51 - √51 = 7.14143
Square Root of 49 - √49 = 7
Square Root of 22 - √22 = 4.69042
Square Root of 33 - √33 = 5.74456

Square Root of 1331 Solved Examples

Example 1: Solve the equation x² − 1331 = 0

Solution:

x² - 1331 = 0 i.e. x² = 1331
x = ±√1331
Since the value of the square root of 1331 is 36.483,
⇒ x = +√1331 or -√1331 = 36.483 or -36.483.
Example 2: If the surface area of a cube is 7986 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 = 7986 in²
⇒ a = ±√1331 in
Since length can't be negative,
⇒ a = √1331
We know that the square root of 1331 is 36.483.
⇒ a = 36.483 in
Example 3: If the area of a circle is 1331π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 1331π in²
⇒ r = ±√1331 in
Since radius can't be negative,
⇒ r = √1331
The square root of 1331 is 36.483.
⇒ r = 36.483 in

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FAQs on the Square Root of 1331

What is the Value of the Square Root of 1331?

The square root of 1331 is 36.48287.

Why is the Square Root of 1331 an Irrational Number?

Upon prime factorizing 1331 i.e. 11³, 11 is in odd power. Therefore, the square root of 1331 is irrational.

What is the Value of 10 square root 1331?

The square root of 1331 is 36.483. Therefore, 10 √1331 = 10 × 36.483 = 364.829.

What is the Square Root of 1331 in Simplest Radical Form?

We need to express 1331 as the product of its prime factors i.e. 1331 = 11 × 11 × 11. Therefore, √1331 = √11 × 11 × 11 = 11 √11. Thus, the square root of 1331 in the lowest radical form is 11 √11.

Is the number 1331 a Perfect Square?

The prime factorization of 1331 = 11³. Here, the prime factor 11 is not in the pair. Therefore, 1331 is not a perfect square.

If the Square Root of 1331 is 36.483. Find the Value of the Square Root of 13.31.

Let us represent √13.31 in p/q form i.e. √(1331/100) = 13.31/10 = 3.648. Hence, the value of √13.31 = 3.648

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