Square root is a mathematical term, which refers to the original value obtained by squaring a number. Simply put, if the square of one number is equal to another number, then this number is the square root of another number. For positive numbers, there are two square roots, and the two square roots are in opposite directions. 8 1 is a positive number. According to the definition of square root, it has two square roots in opposite directions. So the square root of 8 1 is 9.

Some people may mistakenly think that the square root of 8 1 is 9, because in the real number range, the square root of a positive number has only one positive value, while the square root of a negative number has no real number solution. But in the range of complex numbers, negative numbers also have two square roots, and the two square roots are opposite. So when we calculate the square root of 8 1, we need to consider both real and complex numbers, and the result should be 9.

This characteristic of square root is very common in mathematics. For example, we often use the square root to find the square root or the reciprocal of the square of a number. This is very useful in practical applications, such as physics, engineering, economics and other scientific fields.

The application of square root:

1. Calculating portfolio risk: In portfolio theory, the square root is used to calculate portfolio risk. By calculating the variance of the portfolio (that is, the average of the sum of squares of each asset price), we can understand the uncertainty of the portfolio and make more informed investment decisions.

2. Calculating volatility: Square root is also used to calculate the volatility of financial markets. Volatility is an index to measure the range of price changes in financial markets, which is usually used to evaluate the risks and potential benefits of the market. Square root can be used to calculate the estimated value of volatility, thus helping investors to understand the uncertainty and risk level of the market.

3. Calculate the price of financial derivatives: Square root also plays an important role in the pricing model of financial derivatives. For example, in the Black-Scholes model, the square root is used to calculate the volatility and risk-free interest rate of the underlying asset price, thus determining the price of the option. In addition, the square root is also used to calculate the prices of other financial derivatives, such as futures and swap contracts.