Multiplying & Dividing with Surds

A surd is a square root which cannot be reduced to a whole number. Surds are irrational; they are decimals that never end and never repeat, so cannot be written as fractions. Leaving a number in it's surd form is easier and more accurate than writing and rounding the decimal places. We see surds in Pythagoras for example. To simplify surds you look for the largest square number that goes into it. You then split the surd into this square number and what it multiplies to make the original surd number. So root 8 would split into root 4 X root 2 because 4 is the square number and it multiplies by 2 to give the original 8. In this video we use our knowledge of surds to multiply and divide with surds. You treat the number inside the root as one thing, and any numbers outside separately. Think of surds as algebraic expressions. When multiplying surds, you multiply the number inside the root together. When dividing surds, you divide the numbers inside the roots. Remember to simplify the final answer.