could someone explain 'surds' to me (I'm doing A level maths) and just don't get this!?

Answer 1

Surds are numbers left in 'square root form' (or 'cube root form' etc). They are therefore irrational numbers. The reason we leave them as surds is because in decimal form they would go on forever and so this is a very clumsy way of writing them.

Answer 2

When you were doing GCSE or O Level, if you came across something that involved a square-root sign, where the number under the square-root sign wasn't a perfect square, the natural thing to do was to work it out on a calculator.

When you go onto higher Mathematics you can often see answers to certain questions left in surd form i.e. involving a square root sign. This is because a surd is an irrational number and is more accurate in surd form than in decimal form.

When you write a surd in decimal form it is an approximation, and no matter how many decimal places you use, it is still an approximation. Whereas left in surd form it is an exact answer.

You'll find that the same thing happens with Pi. Answers to certain questions are left as some constant multiplied by Pi, because it is more accurate than any decimal approximation.

It's just something you have to get used to in Mathematics

Answer 3

Surds are connected with square roots. In fact surds are numbers that do not have a perfect square.
√9 = 3 and 3² = 9 (not a surd)
√7 cannot be simplified (is a surd)
√100 = 10 and 10² = 100 (not a surd)
√13 cannot be simplied (is a surd)
√25 = 5 and 5² = 25 (not a surd)
√17 cannot be simplified (is a surd)
Hope these examples help.

Answer 4

Not a decimal.

If it is not a whole number leave it as root something.

Remember that you can cancel surds.
If you have root 24 you can make it root 4 x root 6
root 4 = 2
so root 24 = 2 x root 6

Also, if it is a fraction try to get the root on top. You can do this by (if there is a root on the bottom) multiplying the top and bottom by the root that is on the bottom.

Answer 5

Most roots - square roots, cube roots etc of a number are irrational so cannot be written out exactly - thus sqr(2) is approx 1.4142135...............

Thus mathematicians use the root sign (which defaults to square root) to represent the number.

This can be manipulated so, for instance sqr(8) = sqr(2*2*2) = sqr(4).sqr(2) = 2.sqr(2) and sqr(3).sqr(27) = sqr (3*3*3*3) = 3*3 = 9

You can also combine surds with rational numbers e.g. 4 + sqr(3) and we could have for instance (4+sqr(3)) * (4- sqr(3)) which is the difference of two squares (4^2-sqr(3)^2) and comes out as 13.

When dividing by surds it is usually best to have a rational number as the denominator - this is done by either multiplying top and bottom by the surd

e.g 1/sqr(2) = sqr(2) * 1 / (sqr(2)*sqr(2) = sqr(2) / 2

Or if the bottom comprises a surd and a rational number you multiply by the conjugate to generate the difference of two squares.

e.g. 1/(2+ sqr(3)) = (2-sqr(3))/ (2+sqr(3))(2-sqr(3)) = 2- sqr(3)

One of the most famous surds is (1 + sqr(5))/2 = 1.618.... the golden mean or phi

Answer 6

Surds are a group of numbers, and the term refers to those under radical signs. You're probably most familiar with the square-root symbol, but there are many others, including cube-root, 4th-root, etc.

They are written in this manner as they can't be expressed effectively any other way. You can't write them as a fraction, or a whole number, and not even a decimal, because they would basically go on forever.

If you have more specific questions, feel free to email me, ok?

[e-mail]

Answer 7

mathematical quantity that cannot be express as an ordinary number or quantitiy

Answer 8

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Answer 9

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Answer 10

Where did you hear it ??