Question

Can someone help me I'm lost

Answer 1

Answer:   $\sqrt{6}$

This is the same as typing in sqrt(6)

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Explanation:

The square has all four sides the same length, which in this case is $\sqrt{3}$ units.

The diagonal of the square splits it into two identical right triangles.

Use the Pythagorean Theorem to find the hypotenuse x, aka the diagonal.

$a^2 + b^2 = c^2\\\\c = \sqrt{a^2 + b^2}\\\\x = \sqrt{\left(\sqrt{3}\right)^2+\left(\sqrt{3}\right)^2}\\\\x = \sqrt{3+3}\\\\x = \sqrt{6}$

Or you can take the shortcut

$\text{hypotenuse} = (\text{leg})*\sqrt{2}\\\\x = \sqrt{3}*\sqrt{2}\\\\x = \sqrt{3*2}\\\\x = \sqrt{6}$

Which applies to 45-45-90 right triangles.

Answer 2

let's recall that a square has four equal sides, Check the picture below.