Simplify square root by factor method
1. If the number is even, divide by 2. Finding the factor of a number is to find all the numbers that can be multiplied to get this number, which can help you simplify the square root.
If the number is even, then the first thing you can do is divide by 2. In this example, because 98 divided by 2 equals 49, √98 becomes √(2x49). If your number is not divisible by 2, try 3, 4, 5 and so on until you get a factor.
2. Find the complete square factor of the number by finding the factor. See if we can continue to decompose it into the product of factors. 2 is a prime number and can only be divisible by 1 and itself, so you can't find another factor.
But for 49, there are other factors. 49 can be subdivided into 7×7, which is exactly a complete square number. So, you can decompose √(2x49) into √(2x7x7) or √[2(72)], which means we have found the desired perfect square number.
3. Simplify the square root. Because √98=√[2(72)], you can take a 7 from the root sign and simplify it to √98 = 7√2. You can think of this as a "non-square" number, if you can take a number other than the root sign.
So, √49, or √(7 x 7), when you take out the root number, it becomes 7. If you take the 7 outside the root sign in, it will be squared and become 49. So, 98 = 7 √ 2. So for √[2(72)], √72 becomes 7 to the left of √, and 2 in the root sign.
brief introduction
In mathematics, the square root y of the number x refers to a number that satisfies y {2} = x, that is, the square result is equal to X. For example, 4 and -4 are the square roots of 16, because 42? = (? 4)2? = 16。
Any nonnegative real number has a unique nonnegative square root, which is called arithmetic square root or principal square root (English: principal square root), and is denoted as √x, where the symbol √ is called the root sign.
For example, the arithmetic square root of 9 is 3, which is recorded as √9 =3, because? 32? = 3 ? 3 = 9? 3 is negative. The number to find the square root is called the radical sign (English: radical), which is the number or expression under the radical sign, that is, the number 9 in the example.
A positive number x has two opposite square roots: a positive number √x and a negative number -√x, which can be recorded together as.
The square root of a negative number is defined in the complex system. In fact, for any mathematical object that defines the square root operation, "square root" (such as the square root of a matrix) can be considered.