The square root of 500 is expressed as √500 in the radical form and as (500)½ or (500)0.5 in the exponent form. The square root of 500 rounded up to 8 decimal places is 22.36067977. It is the positive solution of the equation x2 = 500. We can express the square root of 500 in its lowest radical form as 10 √5.

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**Square Root of 500:** 22.360679774997898**Square Root of 500 in exponential form:** (500)½ or (500)0.5**Square Root of 500 in radical form:** √500 or 10 √5

1. | What Is the Square Root of 500? |

2. | Is Square Root of 500 Rational or Irrational? |

3. | How to Find the Square Root of 500? |

4. | FAQs on Square Root of 500 |

## What is The Square Root of 500?

The square root of 500 is written as √500 and can be simplified to 10√5.The square root of 500 in decimal form is 22.3606.

## Is Square Root of 500 Rational or Irrational?

The square root of 500 is not an integer and a rational number is a number that can be represented in the form of p/q where q ≠ 0. As the square root of 500 cannot be written in the form of p/q. Hence, the square root of 500 is an irrational number.

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## How to Find the Square Root of 500?

We will now find the square root of 500 using the below two methods:

### Square Root of 500 Using Approximation Method

The two consecutive perfect squares among which 500 lies are 484 (222) and 529 (232).**So, the whole number part of the square root of 500 is 22.The decimal part can be determined by the formula: (Given number – Smaller perfect square) / (Greater perfect square – smaller perfect square) = (500 – 484)/(529 – 484) = 16/45 = 0.35.So, the estimated value of the square root of 500 by the approximation method is 22.35.**

### Square Root of 500 By Long Division

Now we will calculate the square root of 500 by the long division method.

Pair the digits from the right side in pairs of two by putting a bar on top of them. In the case of 500, we will have two pairs 00 and 5(pairing from right).Now we have to find a number(y) whose square is ≤ 5. The value of z will be 2 as 2 × 2 = 4≤ 5.Drag the pair of zero (new dividend becomes 100) and find a number (a) such that 4a × a ≤ 100. The value of a comes out to be 2.Now, add a decimal in the dividend part (100) and quotient part (22) simultaneously. Also, add 3 pairs of zero in the dividend part after the decimal and repeat the above step for the other three pairs of zero as well.

So, we get the value of the square root of √500 = 22.360 by the long division method.

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**Important Notes:**

The number 500 is not a perfect square.The square root of 500 is an irrational number.