Square Root of 160000

The square root is the inverse of the square of the number. 160000 is a perfect square. The square root of 160000 is expressed in both radical and exponential form. In the radical form, it is expressed as √160000, whereas (160000)^(1/2) in the exponential form. √160000 = 400, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.

The prime factorization method is used for perfect square numbers. For perfect squares like 160000, both the prime factorization method and the long division method can be used. Let us now learn the following methods:

• Prime factorization method 
   
• Long division method

The product of prime factors is the prime factorization of a number. Now let us look at how 160000 is broken down into its prime factors.

Step 1: Finding the prime factors of 160000. Breaking it down, we get 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5: 2^6 × 5^4

Step 2: Now we found out the prime factors of 160000. The second step is to make pairs of those prime factors. Since 160000 is a perfect square, the digits of the number can be grouped in pairs. Therefore, calculating √160000 using prime factorization is possible.

Step 3: The square root is obtained by taking one number from each pair, so √160000 = 2^3 × 5^2 = 8 × 25 = 200.

The long division method is particularly useful for both perfect and non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.

Step 1: To begin with, we need to group the numbers from right to left. In the case of 160000, we group it as 16 and 0000.

Step 2: Now we need to find n whose square is less than or equal to 16. We can say n is 4 because 4 × 4 = 16. Now the quotient is 4, and the remainder is 0.

Step 3: Bring down the next pair of zeros, making the new dividend 0000, and bring down another pair making it 000000.

Step 4: The divisor is now 80 (2 × 40) and bringing down the 0s does not change anything as they are zeros. Step 5: Therefore, √160000 = 400.

For a perfect square like 160000, approximation is not needed, but if the number were not a perfect square, approximation methods could be used.

Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping the long division method. Now let us look at a few of those mistakes that students tend to make in detail.

• Square root: A square root is the inverse of squaring a number. Example: 20^2 = 400, and the inverse is √400 = 20.

• Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.

• Perfect square: A perfect square is a number that is the square of an integer. Example: 160000 is a perfect square because it is 400 squared.

• Divisor: A divisor is a number that divides another number completely without leaving a remainder.

• Prime factorization: Prime factorization is the process of expressing a number as a product of its prime factors.