Determine if each root is a rational or irrational number. Explain your reasoning.
A:√ 36
B.√ 78
A rational number is a number that can be written as a ratio of two integers.
A irrational number is a number that cannot be written as the ratio of two integers.
√ 36 = ± 6 = ± 6 / 1
√ 36 is a rational number
√ 78 = ±√ 2 ∙ 3 ∙ 13 = ± √ 2 ∙ √ 3 ∙ √ 13
√ 2 , √ 3 and √ 13 cannot be written as the ratio of two integers so
√ 78 is a irrational number
I don't under stand🤔
thanks🙂
is considered an irrational number. What makes this number irrational? Explain your reasoning.
A: The square root of 36 is a rational number because 36 is a perfect square. It can be expressed as 6, which is a whole number, so it is rational.
B: The square root of 78 is an irrational number because 78 is not a perfect square. It cannot be expressed as a simple fraction or terminating decimal. It involves an endless combination of digits after the decimal point, making it irrational. I guess the number 78 just likes to be complicated!
To determine whether each root is a rational or irrational number, we need to consider if the number inside the square root (√) can be expressed as a ratio of two integers (a rational number) or not (an irrational number).
A: √36
To determine if √36 is a rational or irrational number, we check if 36 can be expressed as a perfect square. 36 can be expressed as 6² since 6 * 6 = 36. Since 6 is an integer, √36 is rational because it can be expressed as the ratio of two integers, in this case, 6/1.
B: √78
To determine if √78 is a rational or irrational number, we need to check if 78 can be expressed as a perfect square. Since 78 cannot be expressed as the square of an integer, we can conclude that √78 is an irrational number.
In summary:
A: √36 is a rational number because it can be expressed as a perfect square (6² = 36).
B: √78 is an irrational number because it cannot be expressed as a perfect square.