Question

How do you simplify \[\sqrt {5200} \] ?

Answer 1

Hint: Square root of a number is a value, which on multiplied by itself gives the original number. Suppose, ‘x’ is the square root of ‘y’, then it is represented as \[x = \sqrt y \] or we can express the same equation as \[{x^2} = y\] . Here we can see that 5200 is not a perfect square. To solve this we factorize the given number.

Complete step-by-step answer:
Given,
 \[\sqrt {5200} \]
294 can be factorized as,
 \[5200 = 1 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 13\]
We can see that 2 is multiplied four times and 5 is multiplied 2 times, we multiply that we get,
 \[5200 = 16 \times 25 \times 13\] .
Then,
 \[ \Rightarrow \sqrt {5200} = \sqrt {16 \times 25 \times 13} \]
Since we know that 16 and 25 is a perfect square we can take this outside of the square root we have,
 \[ = 4 \times 5\sqrt {13} \]
Since 2 and 3 is not a perfect square we can multiply this and we keep it inside the square root,
 \[ = 20\sqrt {13} \] . This is the exact form. We can stop here.
We also put it in the decimal form.
We know that \[\sqrt {13} = 3.605\] and multiplying this with 7 we get,
 \[ = 20 \times 3.605\]
 \[ = 72.10\] . This is the decimal form.
So, the correct answer is “72.10”.

Note: Here \[\sqrt {} \] is the radical symbol used to represent the root of numbers. The number under the radical symbol is called radicand. The positive number, when multiplied by itself, represents the square of the number. To find the factors find the smallest prime number that divides the given number and divide it by that number, and then again find the smallest prime number that divides the number obtained and so on.