Question

Solve x2=1625by inspection. There are two real solutions. Enter the lesser number first. Leave the answers in simplest fraction form. (1 point)

Answer 1

solve x^2=16/25 by inspection

Answer 2

To solve the equation \( x^2 = 1625 \) by inspection, we start by taking the square root of both sides:

\[
x = \pm \sqrt{1625}
\]

Next, let's simplify \( \sqrt{1625} \). First, we factor 1625:

\[
1625 = 25 \times 65 = 25 \times 5 \times 13 = 5^2 \times 5 \times 13 = 5^3 \times 13
\]

Now, we can take the square root:

\[
\sqrt{1625} = \sqrt{5^2 \times 5 \times 13} = 5\sqrt{65}
\]

Thus, the two solutions for \( x \) are:

\[
x = 5\sqrt{65} \quad \text{and} \quad x = -5\sqrt{65}
\]

Since we need to enter the lesser number first, the solutions in simplest fraction form are:

\[
-5\sqrt{65} \quad \text{and} \quad 5\sqrt{65}
\]

So the final answer is:

\[
\boxed{-5\sqrt{65}, 5\sqrt{65}}
\]

Answer 3

To solve the equation \( x^2 = \frac{16}{25} \) by inspection, we can find the square root of both sides.

Taking the square root:

\[
x = \pm \sqrt{\frac{16}{25}}
\]

We can evaluate the square root of the fraction:

\[
\sqrt{\frac{16}{25}} = \frac{\sqrt{16}}{\sqrt{25}} = \frac{4}{5}
\]

Thus, we have two solutions for \( x \):

\[
x = \frac{4}{5} \quad \text{and} \quad x = -\frac{4}{5}
\]

Since we want to list the lesser number first, the solutions are:

\[
-\frac{4}{5} \quad \text{and} \quad \frac{4}{5}
\]

So the final answer is:

\[
\boxed{-\frac{4}{5}, \frac{4}{5}}
\]