Question

Tammy has four cards with irrational numbers on them. She is placing them on a number line. She is determining which card is closest to 7. Which card should she use?

a. 38
b. 67
c. 23
d. 50

Answer 1

To determine the irrational number closest to 7, find the square roots of each option. Since none of the numbers is a perfect square, their square roots are irrational. The square root of 50, approximately 7.071, is closest to 7 on the number line.

Step-by-step explanation:

The values provided in the options are not irrational numbers; however, most likely there is a typo in the question. Assuming the intent was to find the square root of each given number and then to place these square roots on a number line to see which is closest to 7, we can proceed with an approximation.

The square root of an integer is only rational if the integer is a perfect square. In this case, none of the numbers are perfect squares, so we can safely assume the square roots will be irrational numbers.

To approximate:

• For 38 (a), √38 is slightly more than 6 (since 6² = 36).
• For 67 (b), √67 is between 8 and 9 (since 8² = 64 and 9² = 81).
• For 23 (c), √23 is between 4 and 5 (since 4² = 16 and 5² = 25).
• For 50 (d), √50 is exactly 7.071 (since 7² = 49 which is just below 50).

Option d, which is approximately 7.071, is the square root of 50 and is the closest to 7 on a number line.