Simplifying Square Roots

To simplify a square root, make the number inside the square root as small as possible. How to Simplifying Square Roots Rule   where a, b > 0 Simplifying Square Roots for Fractions Rule Surds Surd is a root we can’t simplify further. So √5 is a surd. But √9 = 3 is not a surd. Learn

Law of Sines & Cosines: Formula & Examples

Solving trigonometry’s problem that use right angle can be done by using right triangle and Pythagorean theorem. But, in other problems it does not use right triangle. It uses any triangles. The solution is using law of sines and cosines. It will be more complex than using right triangle but it does not mean difficult.

Inverse Operation

Inverse Operation is an operation that reverses or undo the effect of another operation. Definition of Inverse Operation What are Inverse Operations? Inverse means reverse in position / direction. The word “inverse” comes from the Latin word “inversus” which means to turn inside out or upside down. Inverse operation in mathematics is an operation that undoes what was done by the previous operation. Most

Exterior Angle Theorem

Exterior Angle Theorem For a triangle The exterior angle d equals the angles b plus c. (d = b + c) The exterior angle d is greater than angle b and angle c. (do > bo, do > co) Proof d = b + c : a + b + c = 180° (Because the interior angles of

Commutative, Associative, and Distributive Laws

Commutative Laws Commutative Laws say we can swap numbers over and still get the same answer. Commutative Laws for Addition a + b = b + a Commutative Laws for Multiplication a × b  =  b × a From these laws it follows that any finite sum or product is unaltered by reordering its terms

Finding an Angle in a Right Angled Triangle

We can find an unknown angle in a right-angled triangle, as long as we know the lengths of two of its sides. Use Sine, Cosine or Tangent! Use SOHCAHTOA to help you, like this: How to Finding an Angle in a Right Angled Triangle 1. find the names of the two sides we know Adjacent

Complex Numbers

Imaginary number Imaginary number (when squared give a negative result) i is the unit of imaginary number which is square root of -1 i = √-1, because i2=-1 So, (7i)2 = -7 Definition of Complex Number A Complex Number is a combination of a Real Number and an Imaginary Number Either Part Can Be Zero

Partial Fraction: Definition, Decomposition, Examples

What are partial fractions? Fraction form can’t be ignored in mathematics. Some theorem or topics in mathematics using fraction and also partial fraction. The fractions are possible to be split into two or more simple fraction and it is called partial fraction.   Partial fraction is one of ways to calculate complex fraction to be

Directly and Inversely Proportional

Directly Proportional Directly proportional: when one amount increases, another amount increases at the same rate. The symbol for “directly proportional” is ∝ Inversely Proportional Inversely Proportional: when one value increases, at the same rate that the other decreases. Examples   Directly Proportional Inversely Proportional Have more workers You pay more Work time is shorter How

Irregular Polygon

Regular polygon is a polygon that has all angles equal and all sides equal. So, regular polygon has a = b = c = d = e, and ∠v = ∠w =∠x = ∠y = ∠z Definition of Irregular Polygon Irregular polygon is a polygon that does not have all sides equal and all angles