Question

How would I simplify the square root of 151?

Answer 1

Hint: To solve this question, we should know whether a square root can be simplified or not. For a square root to be simplified, it should satisfy one of the following conditions. The first condition is that the number inside the square root is a perfect square. Else, if the number is not a perfect square, it should have factors that are perfect squares. We will check if the given term satisfies any of these conditions or not.

Complete answer:
The given term is \[\sqrt{151}\]. We know that for a square root term to be simplified it should satisfy one of the two conditions.
The first condition is that the number inside the square root should be a perfect square. We will check if the given term satisfies this condition or not. Here the term inside the square root is 151. 151 is not a not perfect square, hence it does not satisfy this condition.
The second condition is the number inside the square root should have factors that are perfect squares. The number inside the square root is 151. We know that this is a prime number. Hence it does not have any factors except 1 and the number itself. So, this does not satisfy the second condition also.
As this term does not satisfy any of the required conditions. It cannot be simplified further.

Note: Before verifying any of the conditions, check if the number inside the square root is a prime number. If it is then, the square root cannot be simplified further. As prime numbers are not perfect squares nor, they have any factors that are perfect squares.