A surd is a mathematical expression that includes a root, such as a square root or cube root, which cannot be simplified to a rational number.
To simplify a surd, you need to find the largest perfect square that is a factor of the number inside the root. Then, you can take the square root of that perfect square and move it outside the root symbol, leaving the remaining factors inside the root. For example, in the expression 10/√5 + √20, you can simplify √5 to √(5x5) = 5, and √20 to √(4x5) = 2√5. This leaves you with 10/5 + 2√5, which can be further simplified to 2 + 2√5.
A rational number is a number that can be expressed as a ratio of two integers, while an irrational number cannot be expressed as a ratio of integers. Surds, which include roots, are considered irrational numbers.
Yes, surds can be added or subtracted as long as they have the same root. In the expression 10/√5 + √20, both terms have a root of 5, so they can be added together to get 2 + 2√5.
In some cases, surds can be simplified further by finding additional perfect squares that are factors of the number inside the root. However, in the expression 10/√5 + √20, 2 + 2√5 is already in its simplest form.