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Square Root of 233

The square root of 233 is expressed as √233 in the radical form and as (233)^½ or (233)^0.5 in the exponent form. The square root of 233 rounded up to 8 decimal places is 15.26433752. It is the positive solution of the equation x² = 233.

Square Root of 233: 15.264337522473747
Square Root of 233 in exponential form: (233)^½ or (233)^0.5
Square Root of 233 in radical form: √233

Square Root of 233

1.	What is the Square Root of 233?
2.	How to find the Square Root of 233?
3.	Is the Square Root of 233 Irrational?
4.	FAQs

What is the Square Root of 233?

The square root of 233, (or root 233), is the number which when multiplied by itself gives the product as 233. Therefore, the square root of 233 = √233 = 15.264337522473747.

☛ Check: Square Root Calculator

How to Find Square Root of 233?

Square Root of 233 by Long Division Method

Value of √233 by Long Division Method

Explanation:

Forming pairs: 02 and 33
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 33, to the right of the remainder 1. The new dividend is now 133.
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 <= 133. After finding Z, together 2 and Z (5) form a new divisor 25 for the new dividend 133.
Divide 133 by 25 with the quotient as 5, giving the remainder = 133 - 25 × 5 = 133 - 125 = 8.
Now, let's find the decimal places after the quotient 15.
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. 5 + 25 = 30. To the right of 30, find a digit Z (which is 2) such that 30Z × Z <= 800. Together they form a new divisor (302) for the new dividend (800).
Divide 800 by 302 with the quotient as 2, giving the remainder = 800 - 302 × 2 = 800 - 604 = 196.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 233.

Therefore, the square root of 233 by long division method is 15.2 approx.

Is Square Root of 233 Irrational?

The actual value of √233 is undetermined. The value of √233 up to 25 decimal places is 15.26433752247374802525595. Hence, the square root of 233 is an irrational number.

☛ Also Check:

Square Root of 200 - √200 = 14.14214
Square Root of 44 - √44 = 6.63325
Square Root of 51 - √51 = 7.14143
Square Root of 288 - √288 = 16.97056
Square Root of 56 - √56 = 7.48331
Square Root of 324 - √324 = 18
Square Root of 33 - √33 = 5.74456

Square Root of 233 Solved Examples

Example 1: Solve the equation x² − 233 = 0

Solution:

x² - 233 = 0 i.e. x² = 233
x = ±√233
Since the value of the square root of 233 is 15.264,
⇒ x = +√233 or -√233 = 15.264 or -15.264.
Example 2: If the surface area of a cube is 1398 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 = 1398 in²
⇒ a = ±√233 in
Since length can't be negative,
⇒ a = √233
We know that the square root of 233 is 15.264.
⇒ a = 15.264 in
Example 3: If the area of a circle is 233π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 233π in²
⇒ r = ±√233 in
Since radius can't be negative,
⇒ r = √233
The square root of 233 is 15.264.
⇒ r = 15.264 in

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FAQs on the Square Root of 233

What is the Value of the Square Root of 233?

The square root of 233 is 15.26433.

Why is the Square Root of 233 an Irrational Number?

The number 233 is prime. This implies that the number 233 is pairless and is not in the power of 2. Therefore, the square root of 233 is irrational.

If the Square Root of 233 is 15.264. Find the Value of the Square Root of 2.33.

Let us represent √2.33 in p/q form i.e. √(233/100) = 2.33/10 = 1.526. Hence, the value of √2.33 = 1.526

Evaluate 13 plus 16 square root 233

The given expression is 13 + 16 √233. We know that the square root of 233 is 15.264. Therefore, 13 + 16 √233 = 13 + 16 × 15.264 = 13 + 244.229 = 257.229

What is the Square of the Square Root of 233?

The square of the square root of 233 is the number 233 itself i.e. (√233)² = (233)^2/2 = 233.

Is the number 233 a Perfect Square?

The number 233 is prime. This implies that the square root of 233 cannot be expressed as a product of two equal integers. Therefore, the number 233 is not a perfect square.

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