Surds Examples with Solutions
Below are examples of Surds problems with solution.
Example 1: Find product of 4β5 and 2β3.
Solution:
= 4β5 Γ 2β3
= 4 Γ 2 Γ β5 Γ β3
= 8 Γ β(5 Γ 3)
= 8β15
Example 2: Rationalize the denominator 6/(8 + β2).
Solution:
= 6/(8 + β2)
= [6 Γ (8 β β2)]/[(8 + β2)(8 β β2)] [Multiply top and bottom by (8 β β2)]
= [6 Γ (8 β β2)]/(82 β β22)
= [6 Γ (8 β β2)]/62
= 3 Γ (8 β β2)/31
Example 3: Write the expansion of (3 + 2β2)2
Solution:
= (3 + 2β2)2
= 32 + 2 * 3 * 2β2 + (2β2)2
= 9 + 12β2 + 8
= 17 + 12β2
Example 4: What is conjugate of 12β2 + 13
Solution:
Conjugate of 12β2 + 13
= 12β2 β 13
Example 5: If {(24)1/2}k = 256, then find out value of k?
Solution:
{(24)1/2}k = 256
(24Γ1/2)k = 256
22k = 28
2k = 8
k = 4
So, required value of k is 4.
What are Surds?
Surd is a mathematical term used to refer square roots of non-perfect squares. For example, β2, β3, β5 are few examples of Surds. It can also include higher roots like cube roots when these cannot be simplified to a rational number.
In simple terms, Surd is a mathematical term for an irrational number that can be expressed as the root of an integer. Most commonly, surds are used to refer to square roots of non-perfect squares, such as \(\sqrt{2}\), \(\sqrt{3}\), or \(\sqrt{5}\), but they can also include higher roots like cube roots (\(\sqrt[3]{7}\)) when these cannot be simplified to a rational number.
Letβs know more about Surds and itβs types, rules, properties and examples in detail below.
βSurdβ is a Latin word which means deaf or mute. In earlier days, Arabian mathematicians identified rational numbers and irrational numbers as audible and inaudible numbers. Surds are irrational numbers, so they were called asamm (deaf) in the Arabic language, and as surds in the Latin language. Surd is an essential topic in mathematics.
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