Question

1) The value of sqrt(x^2 – 9) is a real and irrational number when x is equal to1) 52) 03) -34) 4

Answer 1

To solve this problem, evaluate the equation for all the values of x in the options.

5:

$\sqrt[]{5^2-9}=\sqrt[]{25-9}=\sqrt[]{16}=4$

4 is a real but a rational number, it means this option is incorrect.

0:

$\sqrt[]{0^2-9}=\sqrt[]{-9}=3i$

3i is not a real number, this option is incorrect.

-3:

$\sqrt[]{(-3)^2-9}=\sqrt[]{9-9}=\sqrt[]{0}=0$

0 is a real but a rational number, this option is incorrect.

4:

$\sqrt[]{4^2-9}=\sqrt[]{16-9}=\sqrt[]{7}$

The square root of 7 is a real and irrational number, it means, this is the correct option.