Multiplying And Dividing Surds Worksheet

Multiplying and dividing surds at a glance

Surds are numbers left in square root form. Surds are used when detailed accuracy is required for a calculation. Surds are irrational numbers, meaning, when written as decimals, they go on forever without any pattern. Rational numbers can be written as fractions with integer numerators and denominators whereas irrational numbers cannot. 

We can multiply and divide surds. When multiplying surds, we use the rule “root a multiplied by root b =  the root of a multiplied by b”. Similarly, when dividing surds we use the rule “root a divided by root b = the root of a divided by b”. 

We can also expand single brackets or double brackets that involve surds. This is done by multiplying every term outside of the brackets by every term inside of the brackets and then simplifying the answer by collecting like terms. We can sometimes simplify surds by taking out factors which are square numbers. A surd is in its simplest form when the number under the root sign has no factors which are square numbers.

Looking forward, students can then progress to additional number worksheets, for example a fractions worksheet or a rounding worksheet.

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