Question

How can you tell whether a square root of a whole number is rational or irrational?

Answer 1

Answer:

To find if the square root of a number is irrational or not, check to see if its prime factors all have even exponents. It also shows us there must be irrational numbers (such as the square root of two) ... in case we ever doubted it!

Step-by-step explanation:hope it help :)

Answer 2

The square root of a whole number is rational only when it is a perfect square and irrational in all other cases.

• A rational number can be expressed in the form p/q where q is not equal to 0.

• The real numbers that cannot be expressed in this form are irrational numbers.

• A perfect square is a number that can be expressed as a square of a given number. For example- 49 is a perfect square because it can be expressed as 7^2.

• When any number is a perfect square, on taking the square root of that number, the result comes out to be an integer. For example- 4 is a perfect square. On taking its square root, the results are 2 and -2 which can be expressed in the form of p/q implying that it is a rational number. For example- 2 can be expressed as 2/1.

• When any number is not a perfect square, on taking its square root, the result is a real number which cannot be expressed in the form p/q. For example- 8 is not a perfect square. On taking its square root, the result is 2.82842 . . . which cannot be expressed in the desired form p/q implying that it is an irrational number.