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.

Mark my answer as brainliest answer.