Define surd tell fiveproblem on Addition, Subtraction,Multiplication of rational number.
Answers
Step-by-step explanation:
In Mathematics, surds are the values in square root that cannot be further simplified into whole numbers or integers. Surds are irrational numbers. The examples of surds are √2, √3, √5, etc., as these values cannot be further simplified. If we further simply them, we get decimal values, such as: √2 = 1.4142135…
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Answer:
numbers, it is known as a mixed surd.
Compound Surds: The addition or subtraction of two or more surds is known as a complex surd.
Binomial Surd: when two surds give rise to one single surd, the resultant surd is known as binomial surds.
Six Rules of Surds
Rule 1: = rXs−−−−√
= r√
x s√
Example:
Simplifying √20.
We know that, √20 = 2 x 2 x 5
√20 = 22 x 5
Here, 4 is the greatest perfect square factor of 20
Therefore,
2–√0
= 22−−√
x 5–√
2–√0
= 2 x 5–√
2–√0
= 25–√
Rule 2: rs−−√
= r√s√
Example:
18169−−−−√
= 18−−√169−−−√
18169−−−−√
= 2×3×3−−−−−−−√13×3−−−−−√
18169−−−−√
= 2×32−−−−−√132−−−√
Here, 9 and 169 are perfect squares.
Therefore, 18169−−−−√
= 32–√13
Rule 3: rs√
= rs√
X s√s√
rs√
= r s√s
The denomination can be rationalized by multiplying the numerator as well as the denominator with the value of the denominator.
Example:
23–√
= 23–√
X 3–√3–√
= 2 3–√3
Rule 4: p r√
± q r√