Question

How do you simplify \[\sqrt {257} \]?

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 257 is not a perfect square. To solve this we factorize the given number.

Complete step-by-step solution:
Given,
\[\sqrt {257} \]
We cannot factorize 257 easily. The square root of 257 cannot be simplified.
We know that 256 is a perfect square. That is \[\sqrt {256} = 16\]. Hence the answer should be very close to 16.
\[\sqrt {257} \] is already in its simplest radical form. Also the square root of 257 is a rational number. We use a calculator to find the square root of 257. We simply type in 257 followed by \[\sqrt x \]to get the answer.
That is \[\sqrt {257} = 16.03121\].

Therefore the correct answer is \[\sqrt {257} = 16.03121\].

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. The square root of the square of a positive number gives the original 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. The set of prime numbers obtained that are multiplied to each other to form the bigger number are called the factors.