## Square & Square Root of 150

## Square of 150

**150² (150×150) = 22500**

The square number of 150 is 22,500. It’s found by multiplying 150 by itself. Understanding square numbers helps in various math concepts like geometry and algebra. Memorizing squares of numbers can simplify calculations and problem-solving in various fields

## Square Root of 150

**√150 = 12.2474487139**

**Or**

**√150 = 12.247 up to three places of decimal**

The square root of 150, denoted as √150, is about 12.247. To find it, you identify the number that, when multiplied by itself, equals 150. This concept, crucial across mathematics, is particularly useful in geometry, algebra, and scenarios where original dimensions need to be determined from area measurements.

**Square Root of 150:** 12.2474487139

**Exponential Form:** 150^½ or 150^0.5

**Radical Form: **√150

## Is the Square Root of 150 Rational or Irrational?

The square root of 150 is irrational because it cannot be expressed as a fraction of two integers. Irrational numbers have non-repeating, non-terminating decimal expansions. The square root of 150 falls into this category, as it is approximately 12.2474487139… when expressed as a decimal. Since 150 is not a perfect square, its square root cannot be simplified to a rational number. This distinction between rational and irrational numbers is fundamental in mathematics and has wide-ranging applications in various fields, including geometry, algebra, and calculus.

A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. Rational numbers include integers, fractions, and terminating or repeating decimals.**Examples: **3/1,5/4.

An irrational number is a real number that cannot be expressed as a fraction of two integers. Irrational numbers have non-repeating and non-terminating decimal expansions.

**Examples: **√2 or √3, and transcendental numbers like π and e.

## Methods to Find Value of Root 150

**Prime Factorization Method:**

Break down 150 into its prime factors: 150=2×3×5² .

Take out pairs of the same prime factors and leave any leftover prime factor outside the square root.

So, √150 = √2×3×5 =5 √6 .**Approximation Method:**

You can estimate the square root of 150 by finding the nearest perfect squares. 150 is between 144 (12) and 169 (13 ).

Since 150 is closer to 144, you can approximate

√150 to be close to 12.(something).**Using a Calculator or Software:**

If precise value is needed, you can simply use a calculator or mathematical software to find the square root of 150.

## Square Root of 150 by Long Division Method

**Start with 150.000000**:- Take numbers in pairs from the right: 50 and 1.

**Divide 1 by a number**:- Find a number that, when multiplied by itself, gives a result less than or equal to 1. This number is 1, with a quotient of 1 and no remainder.

**Double the quotient**:- Multiply the quotient by 2, giving us 2. Our new divisor is 20.

**Bring down 50 for division**:- We divide 50 by 20, resulting in a quotient of 2.

**Find a number for the next divisor**:- We find a number (let’s call it x) that, when added to 20 and then multiplied by x, gives a result less than or equal to 50. We find that 22 works.

**Subtract and bring down**:- Subtract the result of (20 + 22) * 2 from 50, giving us a remainder of 6. Bring down the next pair of zeros, making our new dividend 600.

**Repeat the process**:- Double the previous quotient (2) to get 4, and make this our new divisor (240). Find a number (let’s call it z) that, when added to 240 and then multiplied by z, gives a result less than or equal to 600. We find that 2 works.

**Subtract and bring down again**:- Subtract the result of (240 + 2) * 2 from 600, giving us a remainder of 116. Bring down the next pair of zeros, making our new dividend 11600.

**Continue the process**:- Repeat the steps until you approximate the square root to the desired level of accuracy. The square root of 150 is approximately 12.247 when rounded to three decimal places.

## Is 150 Perfect Square root or Not

No, 150 is not a perfect square because there is no whole number that, when squared, equals 150. The closest perfect squares to 150 are 144 (which is 122122) and 169 (which is 132132). Since 150 lies between these two perfect squares, its square root is an irrational number, meaning it cannot be expressed as a simple fraction or whole number. Therefore, the square root of 150 is an irrational number, approximately equal to 12.247.

## FAQ’S

## What is the square root of 150 to the nearest tenth?

The square root of 150 to the nearest tenth is approximately 12.2. This means that when you multiply 12.2 by itself, you get a value close to 150.

## What perfect square is close to 150?

The closest perfect squares to 150 are 144 (122122) and 169 (132132). 144 is less than 150, while 169 is greater than 150.

## What are prime factors of 150?

The prime factors of 150 are 2, 3, and 5. This means that 150 can be expressed as 2×3×5².

## What two factors equal 150?

Two factors that equal 150 are 10 and 15. These factors multiplied together give the product 150.