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Square Root of 234

The square root of 234 is expressed as √234 in the radical form and as (234)^½ or (234)^0.5 in the exponent form. The square root of 234 rounded up to 7 decimal places is 15.2970585. It is the positive solution of the equation x² = 234. We can express the square root of 234 in its lowest radical form as 3 √26.

Square Root of 234: 15.297058540778355
Square Root of 234 in exponential form: (234)^½ or (234)^0.5
Square Root of 234 in radical form: √234 or 3 √26

Square Root of 234

1.	What is the Square Root of 234?
2.	How to find the Square Root of 234?
3.	Is the Square Root of 234 Irrational?
4.	FAQs

What is the Square Root of 234?

The square root of 234, (or root 234), is the number which when multiplied by itself gives the product as 234. Therefore, the square root of 234 = √234 = 3 √26 = 15.297058540778355.

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How to Find Square Root of 234?

Square Root of 234 by Long Division Method

Value of √234 by Long Division Method

Explanation:

Forming pairs: 02 and 34
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 34, to the right of the remainder 1. The new dividend is now 134.
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 <= 134. After finding Z, together 2 and Z (5) form a new divisor 25 for the new dividend 134.
Divide 134 by 25 with the quotient as 5, giving the remainder = 134 - 25 × 5 = 134 - 125 = 9.
Now, let's find the decimal places after the quotient 15.
Bring down 00 to the right of this remainder 9. The new dividend is now 900.
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 <= 900. Together they form a new divisor (302) for the new dividend (900).
Divide 900 by 302 with the quotient as 2, giving the remainder = 900 - 302 × 2 = 900 - 604 = 296.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 234.

Therefore, the square root of 234 by long division method is 15.2 approx.

Is Square Root of 234 Irrational?

The actual value of √234 is undetermined. The value of √234 up to 25 decimal places is 15.29705854077835449008467. Hence, the square root of 234 is an irrational number.

☛ Also Check:

Square Root of 400 - √400 = 20
Square Root of 149 - √149 = 12.20656
Square Root of 100 - √100 = 10
Square Root of 225 - √225 = 15
Square Root of 900 - √900 = 30
Square Root of 30 - √30 = 5.47723
Square Root of 14 - √14 = 3.74166

Square Root of 234 Solved Examples

Example 1: Solve the equation x² − 234 = 0

Solution:

x² - 234 = 0 i.e. x² = 234
x = ±√234
Since the value of the square root of 234 is 15.297,
⇒ x = +√234 or -√234 = 15.297 or -15.297.
Example 2: If the area of an equilateral triangle is 234√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 = 234√3 in²
⇒ a = ±√936 in
Since length can't be negative,
⇒ a = √936 = 2 √234
We know that the square root of 234 is 15.297.
⇒ a = 30.594 in
Example 3: If the surface area of a cube is 1404 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 = 1404 in²
⇒ a = ±√234 in
Since length can't be negative,
⇒ a = √234
We know that the square root of 234 is 15.297.
⇒ a = 15.297 in

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FAQs on the Square Root of 234

What is the Value of the Square Root of 234?

The square root of 234 is 15.29705.

Why is the Square Root of 234 an Irrational Number?

Upon prime factorizing 234 i.e. 2¹ × 3² × 13¹, 2 is in odd power. Therefore, the square root of 234 is irrational.

If the Square Root of 234 is 15.297. Find the Value of the Square Root of 2.34.

Let us represent √2.34 in p/q form i.e. √(234/100) = 2.34/10 = 1.530. Hence, the value of √2.34 = 1.530

Evaluate 16 plus 9 square root 234

The given expression is 16 + 9 √234. We know that the square root of 234 is 15.297. Therefore, 16 + 9 √234 = 16 + 9 × 15.297 = 16 + 137.674 = 153.674

What is the Square of the Square Root of 234?

The square of the square root of 234 is the number 234 itself i.e. (√234)² = (234)^2/2 = 234.

What is the Square Root of 234 in Simplest Radical Form?

We need to express 234 as the product of its prime factors i.e. 234 = 2 × 3 × 3 × 13. Therefore, √234 = √2 × 3 × 3 × 13 = 3 √26. Thus, the square root of 234 in the lowest radical form is 3 √26.

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