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

• 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.

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.

Square Root of 224 Using Prime Factorization Method

• Prime factorization of 224: 2⁵ × 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

• 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.