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Square Root of 232

The square root of 232 is expressed as √232 in the radical form and as (232)^½ or (232)^0.5 in the exponent form. The square root of 232 rounded up to 10 decimal places is 15.2315462117. It is the positive solution of the equation x² = 232. We can express the square root of 232 in its lowest radical form as 2 √58.

Square Root of 232: 15.231546211727817
Square Root of 232 in exponential form: (232)^½ or (232)^0.5
Square Root of 232 in radical form: √232 or 2 √58

Square Root of 232

1.	What is the Square Root of 232?
2.	How to find the Square Root of 232?
3.	Is the Square Root of 232 Irrational?
4.	FAQs

What is the Square Root of 232?

The square root of 232, (or root 232), is the number which when multiplied by itself gives the product as 232. Therefore, the square root of 232 = √232 = 2 √58 = 15.231546211727817.

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How to Find Square Root of 232?

Square Root of 232 by Long Division Method

Value of √232 by Long Division Method

Explanation:

Forming pairs: 02 and 32
Find a number Y (1) such that whose square is <= 2. Now divide 02 by 1 with quotient as 1.
Bring down the next pair 32, to the right of the remainder 1. The new dividend is now 132.
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 5) such that 2Z × Z <= 132. After finding Z, together 2 and Z (5) form a new divisor 25 for the new dividend 132.
Divide 132 by 25 with the quotient as 5, giving the remainder = 132 - 25 × 5 = 132 - 125 = 7.
Now, let's find the decimal places after the quotient 15.
Bring down 00 to the right of this remainder 7. The new dividend is now 700.
Add the last digit of quotient to divisor i.e. 5 + 25 = 30. To the right of 30, find a digit Z (which is 2) such that 30Z × Z <= 700. Together they form a new divisor (302) for the new dividend (700).
Divide 700 by 302 with the quotient as 2, giving the remainder = 700 - 302 × 2 = 700 - 604 = 96.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 232.

Therefore, the square root of 232 by long division method is 15.2 approximately.

Is Square Root of 232 Irrational?

The actual value of √232 is undetermined. The value of √232 up to 25 decimal places is 15.23154621172781657132282. Hence, the square root of 232 is an irrational number.

☛ Also Check:

Square Root of 29 - √29 = 5.38516
Square Root of 196 - √196 = 14
Square Root of 50 - √50 = 7.07107
Square Root of 97 - √97 = 9.84886
Square Root of 1000 - √1000 = 31.62278
Square Root of 96 - √96 = 9.79796
Square Root of 784 - √784 = 28

Square Root of 232 Solved Examples

Example 1: Solve the equation x² − 232 = 0

Solution:

x² - 232 = 0 i.e. x² = 232
x = ±√232
Since the value of the square root of 232 is 15.232,
⇒ x = +√232 or -√232 = 15.232 or -15.232.
Example 2: If the surface area of a sphere is 928π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 928π in²
⇒ r = ±√232 in
Since radius can't be negative,
⇒ r = √232
The square root of 232 is 15.232.
⇒ r = 15.232 in
Example 3: If the area of an equilateral triangle is 232√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 = 232√3 in²
⇒ a = ±√928 in
Since length can't be negative,
⇒ a = √928 = 2 √232
We know that the square root of 232 is 15.232.
⇒ a = 30.463 in

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FAQs on the Square Root of 232

What is the Value of the Square Root of 232?

The square root of 232 is 15.23154.

Why is the Square Root of 232 an Irrational Number?

Upon prime factorizing 232 i.e. 2³ × 29¹, 2 is in odd power. Therefore, the square root of 232 is irrational.

What is the Square Root of -232?

The square root of -232 is an imaginary number. It can be written as √-232 = √-1 × √232 = i √232 = 15.231i
where i = √-1 and it is called the imaginary unit.

What is the Square of the Square Root of 232?

The square of the square root of 232 is the number 232 itself i.e. (√232)² = (232)^2/2 = 232.

Is the number 232 a Perfect Square?

The prime factorization of 232 = 2³ × 29¹. Here, the prime factor 2 is not in the pair. Therefore, 232 is not a perfect square.

If the Square Root of 232 is 15.232. Find the Value of the Square Root of 2.32.

Let us represent √2.32 in p/q form i.e. √(232/100) = 2.32/10 = 1.523. Hence, the value of √2.32 = 1.523

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