Square Root of 235

The square root of 235 is expressed as √235 in the radical form and as (235)^½ or (235)^0.5 in the exponent form. The square root of 235 rounded up to 5 decimal places is 15.32971. It is the positive solution of the equation x² = 235.

Square Root of 235: 15.329709716755891
Square Root of 235 in exponential form: (235)^½ or (235)^0.5
Square Root of 235 in radical form: √235

Square Root of 235

1.	What is the Square Root of 235?
2.	How to find the Square Root of 235?
3.	Is the Square Root of 235 Irrational?
4.	FAQs

What is the Square Root of 235?

The square root of 235, (or root 235), is the number which when multiplied by itself gives the product as 235. Therefore, the square root of 235 = √235 = 15.329709716755891.

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How to Find Square Root of 235?

Square Root of 235 by Long Division Method

Value of √235 by Long Division Method

Explanation:

Forming pairs: 02 and 35
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 35, to the right of the remainder 1. The new dividend is now 135.
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 <= 135. After finding Z, together 2 and Z (5) form a new divisor 25 for the new dividend 135.
Divide 135 by 25 with the quotient as 5, giving the remainder = 135 - 25 × 5 = 135 - 125 = 10.
Now, let's find the decimal places after the quotient 15.
Bring down 00 to the right of this remainder 10. The new dividend is now 1000.
Add the last digit of quotient to divisor i.e. 5 + 25 = 30. To the right of 30, find a digit Z (which is 3) such that 30Z × Z <= 1000. Together they form a new divisor (303) for the new dividend (1000).
Divide 1000 by 303 with the quotient as 3, giving the remainder = 1000 - 303 × 3 = 1000 - 909 = 91.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 235.

Therefore, the square root of 235 by long division method is 15.3 approx.

Is Square Root of 235 Irrational?

The actual value of √235 is undetermined. The value of √235 up to 25 decimal places is 15.32970971675589165655368. Hence, the square root of 235 is an irrational number.

☛ Also Check:

Square Root of 60 - √60 = 7.74597
Square Root of 900 - √900 = 30
Square Root of 149 - √149 = 12.20656
Square Root of 1521 - √1521 = 39
Square Root of 512 - √512 = 22.62742
Square Root of 289 - √289 = 17
Square Root of 44 - √44 = 6.63325

Square Root of 235 Solved Examples

Example 1: Solve the equation x² − 235 = 0

Solution:

x² - 235 = 0 i.e. x² = 235
x = ±√235
Since the value of the square root of 235 is 15.330,
⇒ x = +√235 or -√235 = 15.330 or -15.330.
Example 2: If the area of a circle is 235π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 235π in²
⇒ r = ±√235 in
Since radius can't be negative,
⇒ r = √235
The square root of 235 is 15.330.
⇒ r = 15.330 in
Example 3: If the area of an equilateral triangle is 235√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 = 235√3 in²
⇒ a = ±√940 in
Since length can't be negative,
⇒ a = √940 = 2 √235
We know that the square root of 235 is 15.330.
⇒ a = 30.659 in

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FAQs on the Square Root of 235

What is the Value of the Square Root of 235?

The square root of 235 is 15.3297.

Why is the Square Root of 235 an Irrational Number?

Upon prime factorizing 235 i.e. 5¹ × 47¹, 5 is in odd power. Therefore, the square root of 235 is irrational.

What is the Square of the Square Root of 235?

The square of the square root of 235 is the number 235 itself i.e. (√235)² = (235)^2/2 = 235.

Evaluate 16 plus 13 square root 235

The given expression is 16 + 13 √235. We know that the square root of 235 is 15.330. Therefore, 16 + 13 √235 = 16 + 13 × 15.330 = 16 + 199.286 = 215.286

What is the Square Root of 235 in Simplest Radical Form?

We need to express 235 as the product of its prime factors i.e. 235 = 5 × 47. Therefore, as visible, the radical form of the square root of 235 cannot be simplified further. Therefore, the simplest radical form of the square root of 235 can be written as √235

What is the Square Root of -235?

The square root of -235 is an imaginary number. It can be written as √-235 = √-1 × √235 = i √235 = 15.329i
where i = √-1 and it is called the imaginary unit.

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