The square source of 224 deserve to be represented in three different forms that room decimal form, radical form, exponential form. The radical kind of 224 is the most frequently used representation of the square root of 224. The square that 224 have the right to be rational or irrational. Now, we will calculate the square root of 224 using various approaches and for better understanding will deal with sample problems as well.

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Square root of 224: √224 = 14.96662Square of 224: (224)2 = 50,176
1.What Is the Square source of 224?
2.Is Square root of 224 rational or Irrational?
3.How to find the Square source of 224?
4.Important note on Square source of 224
5.FAQs on Square source of 224

The square source of 224 in decimal type is 14.96662The square source of 224 is created as √224 in radical form.The square source of 224 is composed as (224)1/2 in exponential form.

Rational numbers room numbers that can be created in the type of p/q wherein q ≠ 0.And the square source of 224 can not be written in the form of p/q.Hence, the square root of 224 is one irrational number.


Square root of 224 utilizing Prime factorization Method

Prime factors of 224 in pairs: (2 × 2) × (2 × 2) × 2 × 7Square source of 224: √224 = √((2 × 2)2 × 2 × 7) = (2 × 2)√(2 × 7) = 4√14

Square root of 224 By long Division

Start splitting the number from the best side right into pairs of two by drawing a line on optimal of them. In the situation of 224, we have two bag 24 and also 2.Now, discover a number(z) whose square is ≤ 2. The worth of z will be 1 together 1 × 1 = 1 ≤ 2.Drag down the next pair (new dividend i do not care 124) and find a number (n) such that 2n × n ≤ 124. The worth of n comes the end to be 4.Now, include a decimal in the dividend (224) and also quotient (14) simultaneously. Also, add 3 bag of zero in the dividend after the decimal (224. 00 00 00) and repeat the over step because that the continuing to be three bag of zero.

So, we gain the worth of the square root of √224 = 14.966 by the long department method.

Explore square roots utilizing illustrations and interactive examples


Important Notes:


The square source of 224 is one irrational number.The number 224 is no a perfect square.

Square root of 224 resolved Examples


Example 1: By which smallest number 224 should be multiplied to do it a perfect square?

Solution:To do 224 a perfect square we need to make the strength of 2 and also 7 even number in the element factorization the 224. And also the prime factorization of 224: 25 × 7.So, to do it a perfect square we have to multiply by 14 then the strength of 2 and 7 will be even numbers.


Example 2: What number must Ria include to 224 to make it a perfect square?

Solution:The square root worth of 224 lie in between 14 and also 15.The square value of 15 is 225.By adding 1 to 224 we have 225.224 + 1 = 225225 is a perfect square number.

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