1)PRACTICAL APPLICATIONS OF SURDS IN DAY-TO-DAY LIFE.. (atleast for 4 marks) ( appropriate answer will be marked as the brainliest)
Answers
Answer:
Surds Definition
Surds are the square roots (√) of numbers which cannot be simplified into a whole or rational number. It cannot be accurately represented in a fraction. In other words, a surd is a root of the whole number that has an irrational value. Consider an example, √2 ≈ 1.414213. It is more accurate if we leave it as a surd √2.
Types of Surds
The different types of surds are as follows:
Simple Surds – A surd that has only one term is called simple surd. Example: √2, √5, …
Pure Surds – Surds which are completely irrational. Example: √3
Similar Surds – The surds having the same common surds factor
Mixed Surds – Surds that are not completely irrational and can be expressed as a product of a rational number and an irrational number
Compound Surds – An expression which is the addition or subtraction of two or more surds
Binomial Surds – A surd that is made of two other surds
Six Rules of Surds
Rule 1:
a×b−−−−√=a−−√×b√
Example:
To simplify √18
18 = 9 x 2 = 32 x 2, since 9 is the greatest perfect square factor of 18.
Therefore, √18 = √(32 x 2)
= √32 x √2
= 3 √2
Rule 2:
ab−−√=a√b√
Example:
√(12 / 121) = √12 / √121
=√(22 x 3) / 11
=√22 x √3 / 11
= 2√3 / 11
Rule 3:
ba√=ba√×a√a√=ba√a
You can rationalize the denominator by multiplying the numerator and denominator by the denominator.
Example:
Rationalise
5/√7
Multiply numerator and denominator by √7
5/√7 = (5/√7) x (√7/√7)
= 5√7/7
Rule 4:
ac√±bc√=(a±b)c√
Example:
To simplify,
5√6 + 4√6
5√6 + 4√6 = (5 + 4) √6
by the rule
= 9√6
Rule 5:
ca+bn√
Multiply top and bottom by a-b √n
This rule enables us to rationalise the denominator.
Example:
To Rationalise
32+2√=32+2√×2−2√2−2√=6−32√4−2 =6−32√2
Rule 6:
ca−bn√
This rule enables you to rationalise the denominator.
Multiply top and bottom by a + b√n
Example:
To Rationalise
32−2√=32−2√×2+2√2+2√=6+32√4−2 =6+32√2
How to Solve Surds?
You need to follow some rules to solve expressions that involve surds. One method is to rationalize the denominators, which helps to eject the surd in the denominator. Sometimes it may be mandatory to find the greatest perfect square factor to solve surds.
Step-by-step explanation:
To Rationalise
32−2√=32−2√×2+2√2+2√=6+32√4−2 =6+32√2
How to Solve Surds?
You need to follow some rules to solve expressions that involve surds. One method is to rationalize the denominators, which helps to eject the surd in the denominator. Sometimes it may be mandatory to find the greatest perfect square factor to solve surds.
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