Breaking down surds to make them managable

Getting to grips with Surds

Secondary Maths

June 28, 2024•2 min read

Understandably, not many people like surds…

A surd is basically a number that when you square root it leaves you with a decimal.

But the key step to a surd is to simplify it first.

So, for example, if we were looking to simplify √63:

Start by writing down all of the factor pairs of 63:

1x63

(2 won’t work)

3 x21

(4 won't work)

(5 won't work)

(6 won't work)

7 x9

Seen as 7x9 is the only pair that involves a square number, we will go with that pair.

Square root the 9 and place that to the left of the surd sign, then sit the 7 underneath giving you the answer: 3√7

Once that bit is conquered, you can look at adding and subtracting surds.

If you were asked: √63 +√28 we already know that √63 is 3√7, so we just need to simplify √28.

The factor pairs of 28 are:

1x28

2x14

4x7

4x7 is the pair with the square number.

So, square root the 4 to give you 2, and place that number on the outside of the surd: 2√7.

This gives you the question: 3√7 + 2√7

3+2 =5,

the 7 stays the same,

so the answer to our question is 5√7.

To subtract, the philosophy is the same except you take one from the other instead of adding.

When you multiply surds you multiply the number on the outside by the number on the inside, so in another example we might have 3√2 x 5√7.

3x5 = 15, this goes on the outside 2x7 = 14, so this goes on the inside

To divide the principle is the same except instead of multiplying the numbers you divide.

It obviously gets harder. Like many things in maths, it lulls you into a false sense of security then turns around and bites you!!

But I hope this makes the initial steps seem easier to contend with.

Dawn Strachan

For the past 20+ years I have been a firm believer that learning should be an enjoyable experience. I appreciate that traditionally education has revolved around worksheets, textbooks, listening to teachers. But a grounding in early years and working with children who had a variety of learning styles from I learned that it is an individual activity that is personal to all of us. We don’t all learn in the same way. Our influences, our experiences, our capabilities all influence how we retain information. But through it all, I believe that if we can make it enjoyable and engaging, they will want to participate. With participation comes practice which in turn boosts skill and confidence. With an increase in skill and confidence comes a willingness to have a go. This in turn leads to more practice which leads to a positive spiral of success. The moral, we need to make learning fun, engaging, use a range of techniques.

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