Square Root of 152
The square root of 152 is expressed as √152 in the radical form and as (152)^{½} or (152)^{0.5} in the exponent form. The square root of 152 rounded up to 7 decimal places is 12.3288280. It is the positive solution of the equation x^{2} = 152. We can express the square root of 152 in its lowest radical form as 2 √38.
 Square Root of 152: 12.328828005937952
 Square Root of 152 in exponential form: (152)^{½} or (152)^{0.5}
 Square Root of 152 in radical form: √152 or 2 √38
1.  What is the Square Root of 152? 
2.  How to find the Square Root of 152? 
3.  Is the Square Root of 152 Irrational? 
4.  FAQs 
What is the Square Root of 152?
The square root of 152, (or root 152), is the number which when multiplied by itself gives the product as 152. Therefore, the square root of 152 = √152 = 2 √38 = 12.328828005937952.
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How to Find Square Root of 152?
Value of √152 by Long Division Method
Explanation:
 Forming pairs: 01 and 52
 Find a number Y (1) such that whose square is <= 1. Now divide 01 by 1 with quotient as 1.
 Bring down the next pair 52, to the right of the remainder 0. The new dividend is now 52.
 Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 2) such that 2Z × Z <= 52. After finding Z, together 2 and Z (2) form a new divisor 22 for the new dividend 52.
 Divide 52 by 22 with the quotient as 2, giving the remainder = 52  22 × 2 = 52  44 = 8.
 Now, let's find the decimal places after the quotient 12.
 Bring down 00 to the right of this remainder 8. The new dividend is now 800.
 Add the last digit of quotient to divisor i.e. 2 + 22 = 24. To the right of 24, find a digit Z (which is 3) such that 24Z × Z <= 800. Together they form a new divisor (243) for the new dividend (800).
 Divide 800 by 243 with the quotient as 3, giving the remainder = 800  243 × 3 = 800  729 = 71.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 152.
Therefore, the square root of 152 by long division method is 12.3 approximately.
Is Square Root of 152 Irrational?
The actual value of √152 is undetermined. The value of √152 up to 25 decimal places is 12.32882800593795290050038. Hence, the square root of 152 is an irrational number.
☛ Also Check:
 Square Root of 60  √60 = 7.74597
 Square Root of 36  √36 = 6
 Square Root of 52  √52 = 7.21110
 Square Root of 676  √676 = 26
 Square Root of 22  √22 = 4.69042
 Square Root of 13  √13 = 3.60555
 Square Root of 85  √85 = 9.21954
Square Root of 152 Solved Examples

Example 1: Solve the equation x^{2} − 152 = 0
Solution:
x^{2}  152 = 0 i.e. x^{2} = 152
x = ±√152
Since the value of the square root of 152 is 12.329,
⇒ x = +√152 or √152 = 12.329 or 12.329. 
Example 2: If the surface area of a cube is 912 in^{2}. 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 = 6a^{2} = 912 in^{2}
⇒ a = ±√152 in
Since length can't be negative,
⇒ a = √152
We know that the square root of 152 is 12.329.
⇒ a = 12.329 in 
Example 3: If the area of an equilateral triangle is 152√3 in^{2}. 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)a^{2} = 152√3 in^{2}
⇒ a = ±√608 in
Since length can't be negative,
⇒ a = √608 = 2 √152
We know that the square root of 152 is 12.329.
⇒ a = 24.658 in
FAQs on the Square Root of 152
What is the Value of the Square Root of 152?
The square root of 152 is 12.32882.
Why is the Square Root of 152 an Irrational Number?
Upon prime factorizing 152 i.e. 2^{3} × 19^{1}, 2 is in odd power. Therefore, the square root of 152 is irrational.
What is the Value of 10 square root 152?
The square root of 152 is 12.329. Therefore, 10 √152 = 10 × 12.329 = 123.288.
What is the Square Root of 152?
The square root of 152 is an imaginary number. It can be written as √152 = √1 × √152 = i √152 = 12.328i
where i = √1 and it is called the imaginary unit.
What is the Square of the Square Root of 152?
The square of the square root of 152 is the number 152 itself i.e. (√152)^{2} = (152)^{2/2} = 152.
If the Square Root of 152 is 12.329. Find the Value of the Square Root of 1.52.
Let us represent √1.52 in p/q form i.e. √(152/100) = 1.52/10 = 1.233. Hence, the value of √1.52 = 1.233