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Square Root of 226

The square root of 226 is expressed as √226 in the radical form and as (226)^½ or (226)^0.5 in the exponent form. The square root of 226 rounded up to 10 decimal places is 15.0332963784. It is the positive solution of the equation x² = 226.

Square Root of 226: 15.033296378372908
Square Root of 226 in exponential form: (226)^½ or (226)^0.5
Square Root of 226 in radical form: √226

Square Root of 226

1.	What is the Square Root of 226?
2.	How to find the Square Root of 226?
3.	Is the Square Root of 226 Irrational?
4.	FAQs

What is the Square Root of 226?

The square root of 226, (or root 226), is the number which when multiplied by itself gives the product as 226. Therefore, the square root of 226 = √226 = 15.033296378372908.

☛ Check: Square Root Calculator

How to Find Square Root of 226?

Square Root of 226 by Long Division Method

Value of √226 by Long Division Method

Explanation:

Forming pairs: 02 and 26
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 26, to the right of the remainder 1. The new dividend is now 126.
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 <= 126. After finding Z, together 2 and Z (5) form a new divisor 25 for the new dividend 126.
Divide 126 by 25 with the quotient as 5, giving the remainder = 126 - 25 × 5 = 126 - 125 = 1.
Now, let's find the decimal places after the quotient 15.
Bring down 00 to the right of this remainder 1. The new dividend is now 100.
Add the last digit of quotient to divisor i.e. 5 + 25 = 30. To the right of 30, find a digit Z (which is 0) such that 30Z × Z <= 100. Together they form a new divisor (300) for the new dividend (100).
Divide 100 by 300 with the quotient as 0, giving the remainder = 100 - 300 × 0 = 100 - 0 = 100.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 226.

Therefore, the square root of 226 by long division method is 15.0 approximately.

Is Square Root of 226 Irrational?

The actual value of √226 is undetermined. The value of √226 up to 25 decimal places is 15.03329637837290827087893. Hence, the square root of 226 is an irrational number.

☛ Also Check:

Square Root of 240 - √240 = 15.49193
Square Root of 37 - √37 = 6.08276
Square Root of 256 - √256 = 16
Square Root of 676 - √676 = 26
Square Root of 75 - √75 = 8.66025
Square Root of 21 - √21 = 4.58258
Square Root of 89 - √89 = 9.43398

Square Root of 226 Solved Examples

Example 1: Solve the equation x² − 226 = 0

Solution:

x² - 226 = 0 i.e. x² = 226
x = ±√226
Since the value of the square root of 226 is 15.033,
⇒ x = +√226 or -√226 = 15.033 or -15.033.
Example 2: If the area of an equilateral triangle is 226√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 = 226√3 in²
⇒ a = ±√904 in
Since length can't be negative,
⇒ a = √904 = 2 √226
We know that the square root of 226 is 15.033.
⇒ a = 30.067 in
Example 3: If the area of a square is 226 in². Find the length of the side of the square.

Solution:

Let 'a' be the length of the side of the square.
⇒ Area of the square = a² = 226 in²
⇒ a = ±√226 in
Since length can't be negative,
⇒ a = √226 = 15.033 in

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FAQs on the Square Root of 226

What is the Value of the Square Root of 226?

The square root of 226 is 15.03329.

Why is the Square Root of 226 an Irrational Number?

Upon prime factorizing 226 i.e. 2¹ × 113¹, 2 is in odd power. Therefore, the square root of 226 is irrational.

What is the Square Root of 226 in Simplest Radical Form?

We need to express 226 as the product of its prime factors i.e. 226 = 2 × 113. Therefore, as visible, the radical form of the square root of 226 cannot be simplified further. Therefore, the simplest radical form of the square root of 226 can be written as √226

What is the Square Root of -226?

The square root of -226 is an imaginary number. It can be written as √-226 = √-1 × √226 = i √226 = 15.033i
where i = √-1 and it is called the imaginary unit.

Evaluate 14 plus 16 square root 226

The given expression is 14 + 16 √226. We know that the square root of 226 is 15.033. Therefore, 14 + 16 √226 = 14 + 16 × 15.033 = 14 + 240.533 = 254.533

What is the Square of the Square Root of 226?

The square of the square root of 226 is the number 226 itself i.e. (√226)² = (226)^2/2 = 226.

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