Question

How do you simplify: square root of 52?

Answer 1

Hint: We are asked to simplify the given expression. The mathematical equivalent of the given expression is \[\sqrt{52}\]. We will first factor the number and pair them up so that it can be brought out of the root. We will rewrite the expression accordingly and hence we will have the simplified form of the given expression.

Complete step by step solution:
According to the given question, we have to simplify the given statement.
The statement we have is, “square root of 52”. If we write this statement in mathematics, we will have the following equivalent, that is, \[\sqrt{52}\]
Square root of a number refers to the value which when multiplied by itself gives the number.
Square root of a number, x is represented by \[\sqrt[2]{x}\] or simply \[\sqrt{x}\].
For example – square root of 25 is 5 or \[\sqrt{25}=5\], this means that if we multiply 5 by itself, that is, 5 multiplied by 5 we get the number 25 (\[5\times 5=25\]).
So, the expression which we have to simplify is,
\[\sqrt{52}\]----(1)
Firstly, we will factor the number and we get the factors as,
\[52=2\times 2\times 13\]
Substituting the factors in equation (1), we get,
\[\sqrt{52}=\sqrt{2\times 2\times 13}\]
We can see that the above expression has two 2’s, we can write it as,
\[\Rightarrow \sqrt{52}=\sqrt{{{2}^{2}}\times 13}\]
Since, the power of 2 is 2, we can take it out and so we get,
\[\Rightarrow \sqrt{52}=2\sqrt{13}\]
Therefore, the simplified form of \[\sqrt{52}=2\sqrt{13}\]

Note: In the above solution, we saw that the square root of a number, x, is represented by \[\sqrt[2]{x}\] or simply \[\sqrt{x}\]. Similarly, the third root of a number, x, is represented by \[\sqrt[3]{x}\]. It is also called the cube root. This means to obtain the number, we will have to multiply the cube root by itself three times.
So, the nth root of a number can be written as \[\sqrt[n]{x}\].