# What Is The Square Root Of 1500, In Simplest Radical Form

The square root of 1500 is expressed as √1500 in the radical form and as (1500)½ or (1500)0.5 in the exponent form. The square root of 1500 rounded up to 5 decimal places is 38.72983. It is the positive solution of the equation x2 = 1500. We can express the square root of 1500 in its lowest radical form as 10 √15.

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**Square Root of 1500:** 38.72983346207417**Square Root of 1500 in exponential form:** (1500)½ or (1500)0.5**Square Root of 1500 in radical form:** √1500 or 10 √15

1. | What is the Square Root of 1500? |

2. | How to find the Square Root of 1500? |

3. | Is the Square Root of 1500 Irrational? |

4. | FAQs |

The square root of 1500, (or root 1500), is the number which when multiplied by itself gives the product as 1500. Therefore, the square root of 1500 = √1500 = 10 √15 = 38.72983346207417.

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### Value of √1500 by Long Division Method

**Explanation:**

Forming pairs: 15 and 00Find a number Y (3) such that whose square is Bring down the next pair 00, to the right of the remainder 6. The new dividend is now 600.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 8) such that 6Z × Z Divide 600 by 68 with the quotient as 8, giving the remainder = 600 – 68 × 8 = 600 – 544 = 56.Now, let's find the decimal places after the quotient 38.Bring down 00 to the right of this remainder 56. The new dividend is now 5600.Add the last digit of quotient to divisor i.e. 8 + 68 = 76. To the right of 76, find a digit Z (which is 7) such that 76Z × Z Divide 5600 by 767 with the quotient as 7, giving the remainder = 5600 – 767 × 7 = 5600 – 5369 = 231.Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1500.

Therefore, the square root of 1500 by long division method is 38.7 approx.

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**☛ Also Check:**

**Example 1: Solve the equation x2 − 1500 = 0**

**Solution:**

x2 – 1500 = 0 i.e. x2 = 1500x = ±√1500Since the value of the square root of 1500 is 38.730,⇒ x = +√1500 or -√1500 = 38.730 or -38.730.

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## FAQs on the Square Root of 1500

### What is the Value of the Square Root of 1500?

The square root of 1500 is 38.72983.

### Why is the Square Root of 1500 an Irrational Number?

Upon prime factorizing 1500 i.e. 22 × 31 × 53, 3 is in odd power. Therefore, the square root of 1500 is irrational.

### What is the Value of 8 square root 1500?

The square root of 1500 is 38.730. Therefore, 8 √1500 = 8 × 38.730 = 309.839.

### What is the Square of the Square Root of 1500?

The square of the square root of 1500 is the number 1500 itself i.e. (√1500)2 = (1500)2/2 = 1500.

### If the Square Root of 1500 is 38.730. Find the Value of the Square Root of 15.

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Let us represent √15 in p/q form i.e. √(1500/100) = 15/10 = 3.873. Hence, the value of √15.0 = 3.873

### What is the Square Root of 1500 in Simplest Radical Form?

We need to express 1500 as the product of its prime factors i.e. 1500 = 2 × 2 × 3 × 5 × 5 × 5. Therefore, √1500 = √2 × 2 × 3 × 5 × 5 × 5 = 10 √15. Thus, the square root of 1500 in the lowest radical form is 10 √15.