The square source of 150 is expressed as √150 in the radical type and as (150)½ or (150)0.5 in the exponent form. The square root of 150 rounded approximately 9 decimal locations is 12.247448714. It is the optimistic solution that the equation x2 = 150. We have the right to express the square root of 150 in its shortest radical form as 5 √6.

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**Square root of 150:**12.24744871391589

**Square root of 150 in exponential form:**(150)½ or (150)0.5

**Square source of 150 in radical form:**√150 or 5 √6

1. | What Is the Square source of 150? |

2. | Is Square source of 150 reasonable or Irrational? |

3. | How to discover the Square root of 150? |

4. | Thinking out Of the Box! |

5. | Important notes on Square source of 150 |

6. | FAQs top top Square source of 150 |

√150 = √(a × a) i m sorry is √150 = √(12.247 × 12.247) or √(-12.247 × -12.247) ⇒ √150 = ±12.247We recognize that on prime factorization, 150 = 2 × 3 × 5 × 5. Thus, in the easiest radical form √150= √(2 × 3 × 5 × 5) = 5√6

Irrational numbers room the real numbers the cannot it is in expressed together the proportion of 2 integers p/q. √150 = 12.24744871391589 and hence, the square root of 150 is one irrational number whereby the numbers after the decimal point go approximately infinity.

The square source of 150 or any kind of number have the right to be calculate in many ways. Two of them room the approximation method and the long department method.

### Square root of 150 through Approximation Method

Take 2 perfect square numbers which are simply smaller 보다 150 and just better than 150. √144 12 Divide 150 by 12 or 13.Let united state divide by 13 ⇒ 150 ÷ 13 = 11.53Find the average of 11.53 and 13.(11.53 + 13) / 2 = 24.53 ÷ 2 = 12.265**√50 ≈ 12.26**

### Square root of 150 by the Long division Method

The long department method helps united state to find a an ext accurate value of the square root of any number. The following are the steps to evaluate the square source of 150 by the long division method.

**Step 1**: create 150.000000. Take it the number in pairs from the right. Us will have 50 together one pair and also 1 was standing alone. Now division 1 by a number such the (number × number) gives ≤ 1.Obtain quotient = 1 and also remainder = 0. Double the quotient. We acquire 2. Us have 20 as our brand-new divisor. Bring under 50 because that division.

**Step 2:**Find a number such that (20 + that number) × the number provides the product ≤ 50. We find 22 × 2 = 44. Subtract this indigenous 50 and also get the remainder as 6. Carry down two zeros. 600 is our brand-new dividend.12 is our quotient. Double it. 240 is our new divisor. Find a number such that (240 + the number) × number gives 600 or much less than that. We will certainly consider 2 as the number. 242 × 2 = 484

**Step 3:**Quotient is 12.2 and the remainder is 116. Lug down the next pair that zeros. 11600 i do not care the brand-new dividend. Double the quotient. 122 × 2 = 244. Have actually 2440 in the place of the brand-new divisor. Discover a number such the (2440 + the number) × number ≤ 11600.We find 2444 × 4 = 9776. Subtract this native 11600 and also get the remainder 1824. Bring down 00.Repeat the measures until us approximate the square source to 3 decimal places.

**√150 = 12.247**

**Explore square roots making use of illustrations and interactive examples: **

**Think Tank**

Did you know that on prime factorization of 150, we get: 2 × 3 × 5 × 5. Thus, 2 and also 3 are the determinants that don"t have actually a pair. For this reason 6 is the least number to it is in multiplied with 150 to do it a perfect square. 6 is the the very least number come be split with 150 to make a perfect square. Can you uncover those perfect squares and their square roots?

**Important Notes**

**Example 1:** How deserve to we prove the 150 is no a perfect square?

**Solution:**

We recognize that the sum of n continually odd numbers = n2. Let united state subtract 150 by continually odd numbers to check if the an outcome is 0. If the repeated subtraction outcomes in 0, that is a perfect square.

150 - 1 = 149149 - 3 = 146146 - 5 = 141141 - 7 = 134134 - 9 = 125125 - 11 = 114114 - 13 = 101 101 - 15 = 8686 - 17 = 6969 - 19 = 5050 - 21 = 29 29 - 23 = 6We have the right to observe the the final result is no 0. Therefore, we have the right to conclude the 150 is not a perfect square. We know that 6 needs to be subtracted indigenous 150 to do it a perfect square. 150 - 6 = 144; √144 = 12

**Example 2:** Evaluate √1.5

**Solution:**

√1.5 = √(150/100)

√150 = 12.247

√100 = 10

√(150/100) = 12.247 / 10 = 1.2247

**√1.5 = 1.2247**

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## FAQs top top the Square source of 150

### What is the value of the Square source of 150?

The square source of 150 is 12.24744.

### Why is the Square root of 150 an Irrational Number?

Upon element factorizing 150 i.e. 21 × 31 × 52, 2 is in strange power. Therefore, the square root of 150 is irrational.

### What is the Square source of -150?

The square root of -150 is an imagine number. It can be composed as √-150 = √-1 × √150 = ns √150 = 12.247iwhere i = √-1 and also it is dubbed the imaginary unit.

### What is the Square of the Square source of 150?

The square that the square source of 150 is the number 150 chin i.e. (√150)2 = (150)2/2 = 150.

### What is the Square root of 150 in simplest Radical Form?

We need to express 150 as the product that its prime determinants i.e. 150 = 2 × 3 × 5 × 5. Therefore, √150 = √2 × 3 × 5 × 5 = 5 √6. Thus, the square root of 150 in the shortest radical type is 5 √6.

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### Is the number 150 a Perfect Square?

The element factorization that 150 = 21 × 31 × 52. Here, the prime element 2 is no in the pair. Therefore, 150 is no a perfect square.