Rationalize the denominator class 8 optional math || surd solutions of Vedanta publications

Rationalize the denominators and simplify:

(a) (7 + sqrt(3))/(7 - sqrt(3))

(b) (2 + sqrt(5))/(2 - sqrt(5))

(c) (sqrt(5) + sqrt(2))/(sqrt(5) - sqrt(2))

3.6

Rationalization of Surds

When the product of two surds is a rational number, each of them is said to be the rationalizing factor of the other.

Example: √3+√2 is rationalizing factor of √3-√2. Then, (√3+√2) x (√3-√2)=3-2 = 1.

The process from which a surd is changed to a rational number by multiplying it with a suitable factor is called the rationalization of the surd..

The following are some basic steps for rationalization.

(i)

Multiply the given surd by a simplest rationalizing factor.

Example: 4√2 × √2 = 4 × 2 = 8

Here √2 is a simplest rationalizing factor.

(ii) Multiply a binomial surd by its conjugate.

Example: √3+√2, its conjugate is √3-√2

Now, (√3 + √2) x (√3-√2) = (√3)² - (√2)² = 3-2 = 1

Here, √3-√2 is a rationalizing factor of √3 + √2.

(iii) When a surd is in the form of quotient, multiply both the numerator and denominator by conjugate of the denominator to make denominator a rational number.

2+√5 Example: 5-2

44

(multiplying numerator and denominator by √5 + 2)

2+55+2 √5-25 5+2 = = (√5+2)²(5)+2.5.2+2 (5)-2 5-4 5+ 4/5 + 4 = 9+4/5 1

[vedanta Excel in Additional Mathematics Book 8

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