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Square Root of 146

The square root of 146 is expressed as √146 in the radical form and as (146)^½ or (146)^0.5 in the exponent form. The square root of 146 rounded up to 10 decimal places is 12.0830459736. It is the positive solution of the equation x² = 146.

Square Root of 146: 12.083045973594572
Square Root of 146 in exponential form: (146)^½ or (146)^0.5
Square Root of 146 in radical form: √146

Square Root of 146

1.	What is the Square Root of 146?
2.	How to find the Square Root of 146?
3.	Is the Square Root of 146 Irrational?
4.	FAQs

What is the Square Root of 146?

The square root of 146, (or root 146), is the number which when multiplied by itself gives the product as 146. Therefore, the square root of 146 = √146 = 12.083045973594572.

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How to Find Square Root of 146?

Square Root of 146 by Long Division Method

Value of √146 by Long Division Method

Explanation:

Forming pairs: 01 and 46
Find a number Y (1) such that whose square is <= 1. Now divide 01 by 1 with quotient as 1.
Bring down the next pair 46, to the right of the remainder 0. The new dividend is now 46.
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 2) such that 2Z × Z <= 46. After finding Z, together 2 and Z (2) form a new divisor 22 for the new dividend 46.
Divide 46 by 22 with the quotient as 2, giving the remainder = 46 - 22 × 2 = 46 - 44 = 2.
Now, let's find the decimal places after the quotient 12.
Bring down 00 to the right of this remainder 2. The new dividend is now 200.
Add the last digit of quotient to divisor i.e. 2 + 22 = 24. To the right of 24, find a digit Z (which is 0) such that 24Z × Z <= 200. Together they form a new divisor (240) for the new dividend (200).
Divide 200 by 240 with the quotient as 0, giving the remainder = 200 - 240 × 0 = 200 - 0 = 200.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 146.

Therefore, the square root of 146 by long division method is 12.0 approx.

Is Square Root of 146 Irrational?

The actual value of √146 is undetermined. The value of √146 up to 25 decimal places is 12.08304597359457206828284. Hence, the square root of 146 is an irrational number.

☛ Also Check:

Square Root of 69 - √69 = 8.30662
Square Root of 140 - √140 = 11.83216
Square Root of 73 - √73 = 8.54400
Square Root of 12 - √12 = 3.46410
Square Root of 136 - √136 = 11.66190
Square Root of 40 - √40 = 6.32456
Square Root of 61 - √61 = 7.81025

Square Root of 146 Solved Examples

Example 1: Solve the equation x² − 146 = 0

Solution:

x² - 146 = 0 i.e. x² = 146
x = ±√146
Since the value of the square root of 146 is 12.083,
⇒ x = +√146 or -√146 = 12.083 or -12.083.
Example 2: If the surface area of a sphere is 584π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 584π in²
⇒ r = ±√146 in
Since radius can't be negative,
⇒ r = √146
The square root of 146 is 12.083.
⇒ r = 12.083 in
Example 3: If the area of a square is 146 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 = 146 in²
⇒ a = ±√146 in
Since length can't be negative,
⇒ a = √146 = 12.083 in

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FAQs on the Square Root of 146

What is the Value of the Square Root of 146?

The square root of 146 is 12.08304.

Why is the Square Root of 146 an Irrational Number?

Upon prime factorizing 146 i.e. 2¹ × 73¹, 2 is in odd power. Therefore, the square root of 146 is irrational.

What is the Value of 16 square root 146?

The square root of 146 is 12.083. Therefore, 16 √146 = 16 × 12.083 = 193.329.

Evaluate 5 plus 2 square root 146

The given expression is 5 + 2 √146. We know that the square root of 146 is 12.083. Therefore, 5 + 2 √146 = 5 + 2 × 12.083 = 5 + 24.166 = 29.166

What is the Square Root of 146 in Simplest Radical Form?

We need to express 146 as the product of its prime factors i.e. 146 = 2 × 73. Therefore, as visible, the radical form of the square root of 146 cannot be simplified further. Therefore, the simplest radical form of the square root of 146 can be written as √146

What is the Square of the Square Root of 146?

The square of the square root of 146 is the number 146 itself i.e. (√146)² = (146)^2/2 = 146.

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