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Square Root of 1176

The square root of 1176 is expressed as √1176 in the radical form and as (1176)^½ or (1176)^0.5 in the exponent form. The square root of 1176 rounded up to 7 decimal places is 34.2928564. It is the positive solution of the equation x² = 1176. We can express the square root of 1176 in its lowest radical form as 14 √6.

Square Root of 1176: 34.292856398964496
Square Root of 1176 in exponential form: (1176)^½ or (1176)^0.5
Square Root of 1176 in radical form: √1176 or 14 √6

Square Root of 1176

1.	What is the Square Root of 1176?
2.	How to find the Square Root of 1176?
3.	Is the Square Root of 1176 Irrational?
4.	FAQs

What is the Square Root of 1176?

The square root of 1176, (or root 1176), is the number which when multiplied by itself gives the product as 1176. Therefore, the square root of 1176 = √1176 = 14 √6 = 34.292856398964496.

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How to Find Square Root of 1176?

Square Root of 1176 by Long Division Method

Value of √1176 by Long Division Method

Explanation:

Forming pairs: 11 and 76
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 76, to the right of the remainder 2. The new dividend is now 276.
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 <= 276. After finding Z, together 6 and Z (4) form a new divisor 64 for the new dividend 276.
Divide 276 by 64 with the quotient as 4, giving the remainder = 276 - 64 × 4 = 276 - 256 = 20.
Now, let's find the decimal places after the quotient 34.
Bring down 00 to the right of this remainder 20. The new dividend is now 2000.
Add the last digit of quotient to divisor i.e. 4 + 64 = 68. To the right of 68, find a digit Z (which is 2) such that 68Z × Z <= 2000. Together they form a new divisor (682) for the new dividend (2000).
Divide 2000 by 682 with the quotient as 2, giving the remainder = 2000 - 682 × 2 = 2000 - 1364 = 636.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1176.

Therefore, the square root of 1176 by long division method is 34.2 approximately.

Is Square Root of 1176 Irrational?

The actual value of √1176 is undetermined. The value of √1176 up to 25 decimal places is 34.29285639896449337476198. Hence, the square root of 1176 is an irrational number.

☛ Also Check:

Square Root of 400 - √400 = 20
Square Root of 1000 - √1000 = 31.62278
Square Root of 37 - √37 = 6.08276
Square Root of 72 - √72 = 8.48528
Square Root of 324 - √324 = 18
Square Root of 15 - √15 = 3.87298
Square Root of 100 - √100 = 10

Square Root of 1176 Solved Examples

Example 1: Solve the equation x² − 1176 = 0

Solution:

x² - 1176 = 0 i.e. x² = 1176
x = ±√1176
Since the value of the square root of 1176 is 34.293,
⇒ x = +√1176 or -√1176 = 34.293 or -34.293.
Example 2: If the surface area of a cube is 7056 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 = 7056 in²
⇒ a = ±√1176 in
Since length can't be negative,
⇒ a = √1176
We know that the square root of 1176 is 34.293.
⇒ a = 34.293 in
Example 3: If the area of a square is 1176 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 = 1176 in²
⇒ a = ±√1176 in
Since length can't be negative,
⇒ a = √1176 = 34.293 in

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FAQs on the Square Root of 1176

What is the Value of the Square Root of 1176?

The square root of 1176 is 34.29285.

Why is the Square Root of 1176 an Irrational Number?

Upon prime factorizing 1176 i.e. 2³ × 3¹ × 7², 2 is in odd power. Therefore, the square root of 1176 is irrational.

If the Square Root of 1176 is 34.293. Find the Value of the Square Root of 11.76.

Let us represent √11.76 in p/q form i.e. √(1176/100) = 11.76/10 = 3.429. Hence, the value of √11.76 = 3.429

What is the Square Root of -1176?

The square root of -1176 is an imaginary number. It can be written as √-1176 = √-1 × √1176 = i √1176 = 34.292i
where i = √-1 and it is called the imaginary unit.

What is the Square of the Square Root of 1176?

The square of the square root of 1176 is the number 1176 itself i.e. (√1176)² = (1176)^2/2 = 1176.

What is the Value of 9 square root 1176?

The square root of 1176 is 34.293. Therefore, 9 √1176 = 9 × 34.293 = 308.636.

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