To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{1} \) = 1

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 1² + 1²
c² = 2
c = \( \sqrt{2} \)

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(2a)(6ab) - (2a²)(2b)
(2 x 6)(a x a x b) - (2 x 2)(a² x b)
(12)(a¹⁺¹ x b) - (4)(a²b)
12a²b - 4a²b
8a²b

The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)² : a = π r².

A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

7a³ - 4a³ = 3a³