+0

# Algebra

0
82
2

For how many real values of x is sqrt(63 - 3*sqrt(x)) an integer?

Jan 25, 2022

#1
+36417
-1

Seven

Jan 25, 2022
#2
+516
+2

If the square root of $$(63 - 3\sqrt{x})$$ is an integer, then it has to be a perfect square.

Here are perfect squares under 63:

49 = 7^2

36 = 6^2

25 = 5^2

16 = 4^2

9 = 3^2

4 = 2^2

1 = 1^2

0 = 0^2

Since there are 8 perfect squares under 63, then there are 8 real values of $$x$$ where the $$\sqrt{(63 - 3\sqrt{x})}$$ is an integer.

Jan 25, 2022