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# What Is The Square Root Of 146 ? Simplify Square Root Of 146

 1. You are watching: What is the square root of 146 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?

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## How to Find Square Root of 146?

### Value of √146 by Long Division Method

Explanation:

Forming pairs: 01 and 46Find a number Y (1) such that whose square is 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 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 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.

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## Square Root of 146 Solved Examples

Example 1: Solve the equation x2 − 146 = 0

Solution:

x2 – 146 = 0 i.e. x2 = 146x = ±√146Since the value of the square root of 146 is 12.083,⇒ x = +√146 or -√146 = 12.083 or -12.083.

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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.