Question

How do you simplify $ \sqrt {224} $ ?

Answer 1

Hint: In order to write the expression into the simplest form, factorize the base part of the value inside the square root such that it contains the maximum number of perfect squares in it to find your desired result.
 $ {(a)^{\dfrac{m}{n}}} $ = $ {({a^m})^{\dfrac{1}{n}}} $
 $ {x^{m + n}} = {x^m} \times {x^n} $

Complete step-by-step answer:
Given a number
 $ \sqrt {224} $
Separating the value $ 224 $ into its factors, So the factors of $ 224 $ comes to be,
 $ 1,2,4,7,8,14,16,28,32,56,112,224 $
Now let’s find the factors who are perfect squares of some number, we got
 $ 1,4,16 $
Let’s consider the largest perfect square form the factors of $ 224 $ and divide it with $ 224 $ ,we get
 $
   = \dfrac{{224}}{{16}} \\
   = 14 \;
  $
From the above we can say that $ 224 = 16 \times 14 $
Replace $ 224 $ as $ 16 \times 14 $ in the original number
 $
   = \sqrt {224} \\
   = \sqrt {16 \times 14} \;
  $
 $ 16 $ can be written as $ {4^2} $
 $ = \sqrt {{4^2} \times 14} $
Taking out $ 4 $ from inside the square root.
 $ = 4\sqrt {14} $
Therefore, $ \sqrt {224} $ in the simplest form $ 4\sqrt {14} $
So, the correct answer is “ $ 4\sqrt {14} $ ”.

Note: In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals and can be written as 3 times 3.