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How do you simplify: square root of 52?

Answer
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Hint: We are asked to simplify the given expression. The mathematical equivalent of the given expression is 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, 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 x2 or simply x.
For example – square root of 25 is 5 or 25=5, this means that if we multiply 5 by itself, that is, 5 multiplied by 5 we get the number 25 (5×5=25).
So, the expression which we have to simplify is,
52----(1)
Firstly, we will factor the number and we get the factors as,
52=2×2×13
Substituting the factors in equation (1), we get,
52=2×2×13
We can see that the above expression has two 2’s, we can write it as,
52=22×13
Since, the power of 2 is 2, we can take it out and so we get,
52=213
Therefore, the simplified form of 52=213

Note: In the above solution, we saw that the square root of a number, x, is represented by x2 or simply x. Similarly, the third root of a number, x, is represented by x3. 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 xn.

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