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Square Root of 1152

The square root of 1152 is expressed as √1152 in the radical form and as (1152)^½ or (1152)^0.5 in the exponent form. The square root of 1152 rounded up to 9 decimal places is 33.941125497. It is the positive solution of the equation x² = 1152. We can express the square root of 1152 in its lowest radical form as 24 √2.

Square Root of 1152: 33.94112549695428
Square Root of 1152 in exponential form: (1152)^½ or (1152)^0.5
Square Root of 1152 in radical form: √1152 or 24 √2

Square Root of 1152

1.	What is the Square Root of 1152?
2.	How to find the Square Root of 1152?
3.	Is the Square Root of 1152 Irrational?
4.	FAQs

What is the Square Root of 1152?

The square root of 1152, (or root 1152), is the number which when multiplied by itself gives the product as 1152. Therefore, the square root of 1152 = √1152 = 24 √2 = 33.94112549695428.

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How to Find Square Root of 1152?

Square Root of 1152 by Long Division Method

Value of √1152 by Long Division Method

Explanation:

Forming pairs: 11 and 52
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 52, to the right of the remainder 2. The new dividend is now 252.
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 <= 252. After finding Z, together 6 and Z (3) form a new divisor 63 for the new dividend 252.
Divide 252 by 63 with the quotient as 3, giving the remainder = 252 - 63 × 3 = 252 - 189 = 63.
Now, let's find the decimal places after the quotient 33.
Bring down 00 to the right of this remainder 63. The new dividend is now 6300.
Add the last digit of quotient to divisor i.e. 3 + 63 = 66. To the right of 66, find a digit Z (which is 9) such that 66Z × Z <= 6300. Together they form a new divisor (669) for the new dividend (6300).
Divide 6300 by 669 with the quotient as 9, giving the remainder = 6300 - 669 × 9 = 6300 - 6021 = 279.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1152.

Therefore, the square root of 1152 by long division method is 33.9 approx.

Is Square Root of 1152 Irrational?

The actual value of √1152 is undetermined. The value of √1152 up to 25 decimal places is 33.94112549695428117124053. Hence, the square root of 1152 is an irrational number.

☛ Also Check:

Square Root of 1296 - √1296 = 36
Square Root of 72 - √72 = 8.48528
Square Root of 75 - √75 = 8.66025
Square Root of 22 - √22 = 4.69042
Square Root of 63 - √63 = 7.93725
Square Root of 96 - √96 = 9.79796
Square Root of 1681 - √1681 = 41

Square Root of 1152 Solved Examples

Example 1: Solve the equation x² − 1152 = 0

Solution:

x² - 1152 = 0 i.e. x² = 1152
x = ±√1152
Since the value of the square root of 1152 is 33.941,
⇒ x = +√1152 or -√1152 = 33.941 or -33.941.
Example 2: If the area of a square is 1152 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 = 1152 in²
⇒ a = ±√1152 in
Since length can't be negative,
⇒ a = √1152 = 33.941 in
Example 3: If the surface area of a cube is 6912 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 = 6912 in²
⇒ a = ±√1152 in
Since length can't be negative,
⇒ a = √1152
We know that the square root of 1152 is 33.941.
⇒ a = 33.941 in

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FAQs on the Square Root of 1152

What is the Value of the Square Root of 1152?

The square root of 1152 is 33.94112.

Why is the Square Root of 1152 an Irrational Number?

Upon prime factorizing 1152 i.e. 2⁷ × 3², 2 is in odd power. Therefore, the square root of 1152 is irrational.

What is the Square Root of -1152?

The square root of -1152 is an imaginary number. It can be written as √-1152 = √-1 × √1152 = i √1152 = 33.941i
where i = √-1 and it is called the imaginary unit.

Is the number 1152 a Perfect Square?

The prime factorization of 1152 = 2⁷ × 3². Here, the prime factor 2 is not in the pair. Therefore, 1152 is not a perfect square.

What is the Square Root of 1152 in Simplest Radical Form?

We need to express 1152 as the product of its prime factors i.e. 1152 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3. Therefore, √1152 = √2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 = 24 √2. Thus, the square root of 1152 in the lowest radical form is 24 √2.

Evaluate 2 plus 2 square root 1152

The given expression is 2 + 2 √1152. We know that the square root of 1152 is 33.941. Therefore, 2 + 2 √1152 = 2 + 2 × 33.941 = 2 + 67.882 = 69.882

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