Surd: An irrational root of a rational number. When you make a post there is a btton in the ribbon called [Math Formula] if you open that and type in 3*sqrt(5) this will be your output. For example, the surd can be simplified by writing = = × = 3. Example: √ 4 (square root of 4) can be simplified (to 2), so it is not a surd! The square root of 45 can also be simplified using surds. In other words, a surd is a root of the whole number that has an irrational value. We stop at this stage seeing that $$2$$ has no square numbers as factors. The object is to define the perimeter of the first, larger, square in surd form. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Surds are the square roots (√) of numbers which cannot be simplified into a whole or rational number. root 45 = root 9 times root 5. so 3 times root 5. zacismyname Apr 12, 2015 #3 +110844 +5 . A surd is said to be in its simplest form when the number under the root sign has no square factors. –5 √6. Consider an example, √2 ≈ 1.414213. You are told that a side (and thus all sides) of the smaller square are root 6 in length (a surd). Surds. Hi Zacismyname . By simplest form, we mean that the number under the square root sign has no square factors (except of course 1). In the second step, we used the third rule listed above. For example $$\sqrt{72}$$ can be reduced to $$\sqrt{4 \times 18} = 2 \sqrt{18}$$. The video below explains that surds are the roots of numbers that are not whole numbers. Example: √ 2 (square root of 2) can't be simplified further so it is a surd. (See following page for discussion of like surds.) The reason we leave them as surds is because in decimal form they would go on forever and so this is a very clumsy way of writing them. It is more accurate if we leave it as a surd … Simplifying surds enables us to identify like surds easily. But $$18$$ still has the factor $$9$$, so we can simplify further: $$2 \sqrt{18} = 2 \sqrt{9 \times 2} = 2 \times 3 \sqrt{2} = 6\sqrt{2}$$. Have a look at some more examples: Number Simplified As a Decimal Surd or not? It cannot be accurately represented in a fraction. General form of a surd: n √a is called a surd of order n, where a is a positive rational number and n is a positive integer greater than 1. When we can't simplify a number to remove a square root (or cube root etc) then it is a surd. They are therefore irrational numbers. Surds are numbers left in 'square root form' (or 'cube root form' etc). Mixed surd: The surds having rational coefficient other than 1 e.g.