What is the result when you divide 13 by the square root of 13?

What is the result when you divide 13 by the square root of 13?

• A. The square root of 13
• B. 13
• C. Square root of 169
• D. 13 divided by 13

Answer: (A)

Dividing a number by its square root collapses to the square root because the square of the square root equals the original number. Here, 13 equals (√13)², so 13 / √13 = (√13)² / √13 = √13. You can also see this by rationalizing: multiply top and bottom by √13 to get 13√13 / 13 = √13. So the result is the square root of 13, which is exactly the option that states √13. Other options would correspond to different values (for example, √169 equals 13, and 13/13 equals 1), so they don’t match the quotient here.

Dividing a number by its square root collapses to the square root because the square of the square root equals the original number. Here, 13 equals (√13)², so 13 / √13 = (√13)² / √13 = √13. You can also see this by rationalizing: multiply top and bottom by √13 to get 13√13 / 13 = √13. So the result is the square root of 13, which is exactly the option that states √13. Other options would correspond to different values (for example, √169 equals 13, and 13/13 equals 1), so they don’t match the quotient here.