Question

How do you find the square root of $28$

Answer 1

In order to determine the square root of the number $28$, first we have to find the factors of number $28$ and choose the largest factor which is a perfect square .Then writing the number in term of that perfect square will result in the simplest form the square root of 28.Since the number $28$is not a perfect square so we cannot find its perfect square root .

Formula:
${(a)^{\dfrac{m}{n}}}$=${({a^m})^{\dfrac{1}{n}}}$

${x^{m + n}} = {x^m} \times {x^n}$

Complete step by step solution:
We a given a number $28$

Square root of any number is actually a number whose square gives back the original number.

So, square root of $28$can be written as,
$= \sqrt {28}$

Now , we’ll Separating the value $28$ into its factors, So the factors of $28$ comes to be,
$1,2,4,7,14,28$

Now let’s find the factors who are perfect squares of any number, we got
$1,4$

Let’s consider the largest perfect square from the factors of $28$and divide it with $28$,we get
$= \dfrac{{28}}{4} \\\ = 7 \\\$
From the above we can say that $28 = 7 \times 4$

Replace $28$as $7 \times 4$ in the original number
$= \sqrt {28} \\\ = \sqrt {7 \times 4} \\\$
$4$ can be written as ${2^2}$
$= \sqrt {{2^2} \times 7}$

Taking out $2$from inside the square root.
$= 2\sqrt 7$

Therefore, the square root of $\sqrt {28}$in the simplest form is equal to $2\sqrt 7$

Additional Information:
A Perfect square is a number which can be easily expressed in terms of square of any number .
For example,$16$is a perfect square of number $4$as${4^2} = 16$

Note: 1. Don’t Forgot to cross check the answer.

2.Factorise the number inside the square root properly to get knowledge of every perfect square.

3.Since 28 is not a perfect square number , so we cannot the perfect square root of this number .We only simply the number and remove the factors which are perfect square from square root