Question

The area of a square is 81square centimeters. First, find the length of a side. Then, find the length of the diagonal?

Answer 1

Part 1:

The length of a side is 9 cm.

The square root of 81 is 9. We have to find the square root bc we know it is a square.

Part 2:

The hypotenuse (or diagonal) is c.

Using the Pythagorean Theorem
$a^{2} + {b}^{2} = {c}^{2}$
you would know that 9 is a and b.

${9}^{2} + {9}^{2} = {c}^{2}$
We know that
${9}^{2} = 81$
so you add 81 to 81.

$81 + 81 = 162$
81 and 81 make 162.

So you know ...

${c}^{2} = 162$
You take the square root of 162.

$\sqrt{162} = 12.73$
well almost.

You can write your answer as

$about \: 12.73 cm$
or
$\sqrt{162} cm$

Hope I helped!