Square Root of 101

The square root of 101 is ±10.0498756211.  Basically, finding the square root is just the inverse of squaring a number and hence, squaring 10.0498756211 will result in 101.  The square root of 101 is written as √101 in radical form. In exponential form, it is written as (101)^1/2 
 

We can find the square root of 11 through various methods. They are:

• Prime factorization method

• Long division method

• Approximation/Estimation method
   

The prime factorization of 101 is done by dividing 101 by prime numbers and continuing to divide the quotients until they can’t be divided anymore. 

• Find the prime factors of 101

• After factorizing 101, make pairs out of the factors to get the square root.

•  if there exist numbers that cannot be made pairs further, we place those numbers with a “radical” sign along with the obtained pairs.

So, Prime factorization of 101 = 101 × 1   

But here in case of 101, no pairs of factors can be obtained and a single 101 is remaining

So, it can be expressed as  √101 

√101 is the simplest radical form of √101 
 

This is a method used for obtaining the square root for non-perfect squares, mainly. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too sometimes.

Follow the steps to calculate the square root of 101:

 Step 1 : Write the number 101, and draw a horizontal bar above the pair of digits from right to left.

Step 2 : Now, find the greatest number whose square is less than or equal to 1. Here, it is1, Because 1²=1 < 1.

Step 3 : Now divide 1 by 1 such that we get 1 as quotient and then multiply the divisor with the quotient, we get 1

Step 4: Subtract 1 from 1. Bring down 0 and 1 and place it beside the difference 0.

Step 5: Add 1 to same divisor, 1. We get 2.

Step 6: Now choose a number such that when placed at the end of 2, a 2-digit number will be formed. Multiply that particular number by the resultant number to get a number less than 1. Here, that number is 0. 

20×0=0<1.

Step 7: Subtract 1-0=1. Add a decimal point after the new quotient 10, again, bring down two zeroes and make 1 as 100. Simultaneously add the unit’s place digit of 20, i.e., 0 with 20. We get here, 20. Apply Step 5 again and again until you reach 0. 

We will show two places of precision here, and so, we are left with the remainder, 17599 (refer to the picture), after some iterations and keeping the division till here, at this point 

             
Step 8 : The quotient obtained is the square root. In this case, it is 10.049….

Approximation or estimation of square root is not the exact square root, but it is an estimate.Here, through this method, an approximate value of square root is found by guessing.

Follow the steps below:

Step 1: Find the nearest perfect square number to 101. Here, it is 100 and 121.

Step 2: We know that, √100=10 and √121=11. This implies that √101 lies between 10 and 11.

Step 3: Now we need to check √101 is closer to 10 or 11. Let us consider 10 and 10.5. Since (10)²=100 and (10.5)²=110.25. Thus, √101 lies between 10 and 10.5.

Step 4: Again considering precisely, we see that  √101 lies close to (10)²=100. Find squares of (10.02)²=100.4 and (10.1)²= 112.11.

We can iterate the process and check between the squares of 10.03 and 10.05 and so on.

We observe that √101=10.049…

• Exponential form:  An algebraic expression that includes an exponent. It is a way of expressing the numbers raised to some power of their factors. It includes continuous multiplication involving base and exponent. Ex: 2 × 2 × 2 × 2 = 16 Or, 2⁴ = 16, where 2 is the base, 4 is the exponent 

• Prime Factorization:  Expressing the given expression as a product of its factors. Ex: 48=2 × 2 × 2 × 2 × 3

• Prime Numbers: Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....

• Rational numbers and Irrational numbers: The Number which can be expressed as p/q, where p and q are integers and q not equal to 0 are called Rational numbers. Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers. 

• Perfect and non-perfect square numbers: Perfect square numbers are those numbers whose square roots do not include decimal places. Ex: 4,9,25 Non-perfect square numbers are those numbers whose square roots comprise decimal places. Ex :3, 8, 24