The square root of 1250 is expressed as √1250 in the radical form and as (1250)½ or (1250)0.5 in the exponent form. The square root of 1250 rounded up to 10 decimal places is 35.3553390593. It is the positive solution of the equation x2 = 1250. We can express the square root of 1250 in its lowest radical form as 25 √2.

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**Square Root of 1250:** 35.35533905932738**Square Root of 1250 in exponential form:** (1250)½ or (1250)0.5**Square Root of 1250 in radical form:** √1250 or 25 √2

1. | What is the Square Root of 1250? |

2. | How to find the Square Root of 1250? |

3. | Is the Square Root of 1250 Irrational? |

4. | FAQs |

The square root of 1250, (or root 1250), is the number which when multiplied by itself gives the product as 1250. Therefore, the square root of 1250 = √1250 = 25 √2 = 35.35533905932738.

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### Value of √1250 by Long Division Method

**Explanation:**

Forming pairs: 12 and 50Find a number Y (3) such that whose square is Bring down the next pair 50, to the right of the remainder 3. The new dividend is now 350.Add the last digit of the quotient (3) to the divisor (3) i.e. 3 + 3 = 6. To the right of 6, find a digit Z (which is 5) such that 6Z × Z Divide 350 by 65 with the quotient as 5, giving the remainder = 350 – 65 × 5 = 350 – 325 = 25.Now, let's find the decimal places after the quotient 35.Bring down 00 to the right of this remainder 25. The new dividend is now 2500.Add the last digit of quotient to divisor i.e. 5 + 65 = 70. To the right of 70, find a digit Z (which is 3) such that 70Z × Z Divide 2500 by 703 with the quotient as 3, giving the remainder = 2500 – 703 × 3 = 2500 – 2109 = 391.Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1250.

Therefore, the square root of 1250 by long division method is 35.3 approx.

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**☛ Also Check:**

**Example 1: Solve the equation x2 − 1250 = 0**

**Solution:**

x2 – 1250 = 0 i.e. x2 = 1250x = ±√1250Since the value of the square root of 1250 is 35.355,⇒ x = +√1250 or -√1250 = 35.355 or -35.355.

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## FAQs on the Square Root of 1250

### What is the Value of the Square Root of 1250?

The square root of 1250 is 35.35533.

### Why is the Square Root of 1250 an Irrational Number?

Upon prime factorizing 1250 i.e. 21 × 54, 2 is in odd power. Therefore, the square root of 1250 is irrational.

### Evaluate 3 plus 19 square root 1250

The given expression is 3 + 19 √1250. We know that the square root of 1250 is 35.355. Therefore, 3 + 19 √1250 = 3 + 19 × 35.355 = 3 + 671.751 = 674.751

### If the Square Root of 1250 is 35.355. Find the Value of the Square Root of 12.5.

Let us represent √12.5 in p/q form i.e. √(1250/100) = 12.5/10 = 3.536. Hence, the value of √12.5 = 3.536

### What is the Square Root of 1250 in Simplest Radical Form?

We need to express 1250 as the product of its prime factors i.e. 1250 = 2 × 5 × 5 × 5 × 5. Therefore, √1250 = √2 × 5 × 5 × 5 × 5 = 25 √2. Thus, the square root of 1250 in the lowest radical form is 25 √2.

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### What is the Square Root of -1250?

The square root of -1250 is an imaginary number. It can be written as √-1250 = √-1 × √1250 = i √1250 = 35.355iwhere i = √-1 and it is called the imaginary unit.