Surds

Definition

• What is a SURD?
• An irrational nth root.
• Any mathematical expression (square root, cube root or higher root) which cannot be written as a common fraction
• An irrational number is
• Any real number that cannot be expressed as a ratio a/b, where a and b are integers and b is non-zero.
• Informally
• An irrational number cannot be represented as a simple (common) fraction.
• Irrational numbers are those real numbers that cannot be represented as terminating or repeating decimals.

multiplying surds

• when the number under the root is the same then the product is just the number under the root sign
• multiply the numbers under the root and simplify further if needed
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rationalising the denominator 1

• if the only number in the denominator is a surd you need to multiply both the numerator by that surd
• since a surd multiplied by the same surd gets rid of the root sign, in the denominator all you need to write is the number which was previously a surd
• for the numerator follow the operations to get the answer
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rationalising the denominator 2

• is the denominator includes other numbers and operations as well as a surd then for now all you need to do is multiply the conjugate of the denominator( including the surd) by both the numerator and denominator
• as the surds in the denominator will remove the radical sign you ned to apply necessary functions to it using the operations and numbers given in the denominator
• 

Simplifying surds

• a square root radical is simplified, or in its simplest form, when the radicand has no square factors.
• how to simplify- https://www.youtube.com/watch?v=YMny-hM1NNA
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