SQUARE ROOT OF 225

The square root of 225 is ±15, where 15 is the positive solution of the equation x² = 225. Finding the square root is just the inverse of squaring a number and hence, squaring 15 will result in 225. The square root of 225 is written as √225 in radical form, where the ‘√’  sign is called the  “radical” sign. In exponential form, it is written as (225)^1/2 
 

We can find the square root of 225 through various methods. They are:
i) Prime factorization method
ii) Long division method
iii) Repeated subtraction method.
 

The prime factorization of 225 can be found by dividing the number by prime numbers and continuing to divide the quotients until they can’t be separated anymore.

After factorizing 225, make pairs out of the factors to get the square root.

So, Prime factorization of 225 = 3 × 5 × 3 × 5

Square root of 225 = √[3 × 3 ×5 × 5] = 3 × 5= 15

This method is 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 225:

Step 1: Write the number 225 and draw a 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 2. Here, it is 1 because 1²=1 < 2.

Step 3: now divide 225 by 1 (the number we got from Step 2) such that we get 1 as a quotient, and we get a remainder.  

Double the divisor 1, we get 2, and then the largest possible number A1=5 is chosen such that when 5 is written beside the new divisor 2, a 2-digit number is formed →25, and multiplying 5 with 25 gives 125, which when subtracted from 125, gives 0.

Repeat this process until you reach the remainder of 0. 

Step 4: The quotient obtained is the square root of 225. In this case, it is 15.

We know that the sum of the first n odd numbers is n². We will use this fact to find square roots through the repeated subtraction method.

Furthermore, we just have to subtract consecutive odd numbers from the given number, starting from 1. The square root of the given number will be a count of the number of steps required to obtain 0.

Here are the steps:

Step 1: Take the number 225 and then subtract the first odd number from it. Here, in this case, it is 225-1=224.

Step 2: we have to subtract the next odd number from the obtained number until it comes zero as a result. Now take the obtained number (from Step 1), i.e., 224, and again subtract the next odd number after 1, from 3, i.e.,224-3=221. Like this, we have to proceed further.

Step 3: Now we have to count the number of subtraction steps it takes to yield 0 finally. Here, in this case, it takes 15 steps. So, the square root is equal to the count, i.e., the square root of 225 is ±15.

• 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, 2 4 = 16, where 2 is the base, 4 is the exponent

• 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