Solve x2= 2564

Question

by inspection. There are 2 real solutions. Enter the lesser number first. Leave the answers in simplest fraction form.

(1 point)
The first solution is x=

The second solution is x =

Question

Answer 1

To solve the equation \( x^2 = 2564 \) by inspection, we need to find the square roots of 2564.

The two real solutions for this equation are given by:

1. \( x = \sqrt{2564} \)
2. \( x = -\sqrt{2564} \)

Calculating \( \sqrt{2564} \):

First, we can try to simplify the square root to find the simplest fraction:

\[ 2564 = 4 \times 641 \]

Taking the square root:

\[ \sqrt{2564} = \sqrt{4 \times 641} = \sqrt{4} \times \sqrt{641} = 2\sqrt{641} \]

Thus, the two solutions are:

1. \( x = -2\sqrt{641} \)
2. \( x = 2\sqrt{641} \)

Since we are instructed to enter the lesser number first, the answers are:

The first solution is \( x = -2\sqrt{641} \).

The second solution is \( x = 2\sqrt{641} \).