Question 1

What is the formula for the Pythagorean Theorem?

Accepted Answer

In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: a² + b² = c². To solve for hypotenuse: c = √(a² + b²). To solve for a leg: a = √(c² - b²) or b = √(c² - a²).

Question 2

How does this calculator simplify radicals automatically?

Accepted Answer

The calculator performs prime factorization on the radicand to extract all perfect square factors. For instance, √20 = √(4 × 5) = 2√5, and √18 = √(9 × 2) = 3√2, giving you the exact simplest radical form.

Question 3

What are common Pythagorean triples?

Accepted Answer

Common primitive Pythagorean triples include (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), (9, 40, 41), and (20, 21, 29). Multiplying by any positive integer creates derived triples such as (6, 8, 10).