Question

Write the conjugates of
√5 - 3​

Answer 1

Answer:

We know that the when sum of two terms and the difference of the same two terms are multiplied, the product is always a rational number.

Let us apply this concept to a binomial surd (5+

3

).

When we multiply this with the difference of the same two terms, that is, with (5−

3

), the product is:

(5+

3

)(5−

3

)=(5)

2

−(

3

)

2

=25−3=22(∵a

2

−b

2

=(a+b)(a−b))

Since 22 is a rational number.

Hence, (5−

3

) is the conjugate of (5+

3

)

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Answer 2

SOLUTION :-

We know that the when sum of two terms and the difference of the same two terms are multiplied, the product is always a rational number.

Let us apply this concept to a binomial surd

$( \: 5 \: + \: \sqrt{3} \: ).$

When we multiply this with the difference of the same two terms, that is, with

$( \: 5 \: - \: \sqrt{3} \: )$

, the product is:

$( \: 5 \: + \: \sqrt{3} \: )( \: 5 \: - \: \sqrt{3} \: ) = (5)^{2} - ( \sqrt{3} \: ) ^{2} = 25 \: - \: 3 = 22 \: (∴a^{2} \: - \: b ^{2} = (a \: + \: b)(a \: - \: b))$

Since 22 is a rational number.

Hence,

$(5 \: - \: \sqrt{3} )$

is the conjugate of

$(5 \: + \: \sqrt{3} )$