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Square Root of 224
The square root of 224 can be represented in three different forms that are decimal form, radical form, exponential form. The radical form of 224 is the most commonly used representation of the square root of 224. The square of 224 can be rational or irrational. Now, we will calculate the square root of 224 using different approaches and for better understanding will solve sample problems as well.
 Square root of 224: √224 = 14.96662
 Square of 224: (224)^{2} = 50,176
1.  What Is the Square Root of 224? 
2.  Is Square Root of 224 Rational or Irrational? 
3.  How to Find the Square Root of 224? 
4.  Important Notes on Square Root of 224 
5.  FAQs on Square Root of 224 
What is the Square Root of 224?
 The square root of 224 in decimal form is 14.96662
 The square root of 224 is written as √224 in radical form.
 The square root of 224 is written as (224)^{1/2} in exponential form.
Is Square Root of 224 Rational or Irrational?
Rational numbers are numbers that can be written in the form of p/q where q ≠ 0.
And the square root of 224 cannot be written in the form of p/q.
Hence, the square root of 224 is an irrational number.
How to Find the Square Root of 224?
Square Root of 224 Using Prime Factorization Method
 Prime factorization of 224: 2^{5} × 7
 Prime factors of 224 in pairs: (2 × 2) × (2 × 2) × 2 × 7
 Square root of 224: √224 = √((2 × 2)^{2} × 2 × 7) = (2 × 2)√(2 × 7) = 4√14
Square Root of 224 By Long Division
 Start dividing the digits from the right side into pairs of two by drawing a line on top of them. In the case of 224, we have two pairs 24 and 2.
 Now, find a number(z) whose square is ≤ 2. The value of z will be 1 as 1 × 1 = 1 ≤ 2.
 We get the quotient and the remainder as 1. Now, add the divisor z with itself and get the new divisor 2z (2).
 Drag down the next pair (new dividend becomes 124) and find a number (n) such that 2n × n ≤ 124. The value of n comes out to be 4.
 Now, add a decimal in the dividend (224) and quotient (14) simultaneously. Also, add 3 pairs of zero in the dividend after the decimal (224. 00 00 00) and repeat the above step for the remaining three pairs of zero.
So, we get the value of the square root of √224 = 14.966 by the long division method.
Explore square roots using illustrations and interactive examples
 Square root of 221
 Square root of 22
 Square root of 225
 Square root of 24
 Square root of 144
 Square root of 44
 Square root of 441
Important Notes:
 The square root of 224 is an irrational number.
 The number 224 is not a perfect square.
 The square root of 224 is an imaginary number.
Square Root of 224 Solved Examples

Example 1: By which smallest number 224 must be multiplied to make it a perfect square?
Solution:
To make 224 a perfect square we have to make the power of 2 and 7 even number in the prime factorization of 224. And the prime factorization of 224: 2^{5} × 7.
So, to make it a perfect square we have to multiply by 14 then the power of 2 and 7 will be even numbers. 
Example 2: What number should Ria add to 224 to make it a perfect square?
Solution:
The square root value of 224 lie between 14 and 15.
The square value of 15 is 225.
By adding 1 to 224 we have 225.
224 + 1 = 225
225 is a perfect square number.
FAQs on Square Roots of 224
What is the negative square root of 224?
The negative square root of 224 is 14.96662
What is the square of 224?
The square of 224 is (224)^{2} = 50,176.
What is the prime factorization of 224?
The prime factorization of 224 is: 2^{5} × 7
Is the square root of 224 a rational number?
No, the square root of 224 is not a rational number.
Because the square root of 224 is a nonterminating and nonrepeating number thus, can’t be expressed in p/q form.
Is the number 224 a perfect square?
No, 224 is not a perfect square
Because the square root of 224 is an irrational number.
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