Surds - Intro & How To Simplify

This lesson covers:

  1. How to simplify surds 
  2. E.g. 'Write 48\sqrt{48} in the form of k3\sqrt{3}, where k is an integer'

Is a surd a rational or irrational number?

Irrational

Rational

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Which for the following describes a surd?

An irrational root of a rational number 

A rational root of an irrational number 

A rational root of a rational number 

An irrational root of an irrational number 

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Does √9 count as a surd?

No, because 9 is a square number so can be square rooted to give an integer.

Yes, because the 9 is in a square root sign.

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What is 9\sqrt{9}

3

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Evaluate √7×√5
\sqrt{35}

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Evaluate √11×√3
\sqrt{33}

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Evaluate √30÷√5
\sqrt{6}

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Evaluate √21÷√7
\sqrt{3}

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Write √50 in the form k√2 where k is an integer
5\sqrt{2}

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Write √48 in the form k√3 where k is an integer
4\sqrt{3}

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Write √27 in the form k√3 where k is an integer
3\sqrt{3}

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Express √72 in its simplest form
6\sqrt{2}

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Express √300 in its simplest form
10\sqrt{3}

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Write 4√20 in the form k√5 where k is an integer
8\sqrt{5}

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