A surd is a square root that is an irrational number. The number is only exact when left in surd form, if you use a calculator to give you the exact value, it becomes in-exact.

Example of a surd: √3 . If I ask my calculator what √3 is, it'll say 1.73205060757, which has truncated a load of digits. So it's best to manipulate this number in surd form.

Some rules when manipulating surds -

√a * √b = √(a * b)
√a divided by √b = √(a divided by b)

Surd (?), a. [L. surdus deaf (whence the meaning, deaf to reason, irrational), perhaps akin to E. swart. Cf. Sordine.]

1.

Not having the sense of hearing; deaf.

[Obs.] "A surd . . . generation."

Sir T. Browne.

2.

Unheard.

[Obs.]

Kenrick.

3. Math.

Involving surds; not capable of being expressed in rational numbers; radical; irrational; as, a surd expression or quantity; a surd number.

4. Phonetics

Uttered, as an element of speech, without tone, or proper vocal sound; voiceless; unintonated; nonvocal; atonic; whispered; aspirated; sharp; hard, as f, p, s, etc.; -- opposed to sonant. See Guide to Pronunciation, §§169, 179, 180.

Surd, n. Math.

1.

A quantity which can not be expressed by rational numbers; thus, √2 is a surd.

2. Phon.

A surd element of speech. See Surd, a., 4.

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