Question

Write the conjugate of the following surds : 7-√3
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Answer 1

Step-by-step explanation:

the sum and the difference of two simple quadratic surds 4√7and √2 are 4√7 + √2 and 4√7 - √2 respectively. Therefore, two surds (4√7 + √2) and (4√7 - √2) are conjugate to each other.

Answer 2

༒࿐៚ 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 applying this Concept to a binomial Surd (7-√3).

When we Multiply this with the difference of the Same two terms, that is, With (7-√3), the Product is :

$(7 + \sqrt{3} )(7 - \sqrt{3} ) = (7 {)}^{2} - ( \sqrt{3} {)}^{2} = 49 - 3 = 46.$

$( \: {a}^{2} - {b}^{2} = (a + b)(a - b)$

Since, 46 is a rational Number.

Hence, (7+√3) is a Conjugate of (7-√3)