Is √16 an irrational number?

Answer: No, √16 is not an irrational number, i.e. √16 is an rational number as it is easily represented in p/q format where p and q are integers and q is not equal to zero , and most important point is p and q are coprime , √16 = ±4 (±4/1).

Perfect squares have rational square roots. Square root of the perfect square 16 is 4.

• √16 = ±4/1 = ±4

Therefore √16 is not an irrational number.

What is an Irrational Number?

Numbers which are not rational numbers are called irrational numbers. Now, let us elaborate, we can say that the numbers which can not be expressed in p/q form where p and q are integers ,q is not equal to zero, both p and q are coprime.

Irrational numbers have endless non-repeating digits after the decimal point. Below is an example of an irrational number:

Example: √8 = 2.828…

Why √16 is Rational and not Irrational?

A perfect square is an integer (whole number) that can be obtained by squaring another integer. In other words, it’s like taking a square pizza and cutting it into rows and columns of equal-sized square slices.

Examples: 4 = (2 × 2), 9 = (3 × 3), 16 = (4 × 4).

Square root of any perfect square is always rational. This means the square root can be expressed as a whole number or a fraction.

Therefore, √16 = ±4. Since ±4 can be written as ±4/1 (both numerator and denominator are integers) and there GCD is 1 and 1 isn’t equal to zero, √16 is a rational number and not an irrational number.

Similar Questions

Question 1: Is √8 an Irrational number?

Solution: 

Taking into account that 8 is not a perfect square, we may decide whether √8 is rational or irrational. The square root of 8 is irrational as 8 is not an integer ,when we try to find square root of 8 then the decimal expansion we get neither terminates nor repeats.

Put another way, √8 is an irrational number as it cannot be written as a fraction of two integers (p/q). √8 is an irrational number as a result.

Question 2: Is √4 an Irrational number?

Solution:

No, √4 is not an irrational number. √4 is equal to ±2, which is a rational number. In fact, √4 is a perfect square root, and perfect square roots are always rational. The square root of 4 can be expressed as the ratio 2/1, confirming its rational nature.

Question 3: Is the square root of 144 a rational number?

Solution:

Yes, the square root of 144 is a rational number since √144 = ±12.