Question

Rationalise 4+ root 3 upon 4- root 3 + 4- root 3 upon 4+root 3

Answer 1

Using

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

so,

=$(4 + \sqrt{3})(4 - \sqrt{3)}$

= ${4}^{2} - ( \sqrt{3)^{2} }$

= 16-3

= 13

Answer 2

Answer:

The final answer of the given expression is 13.

Step-by-step explanation:

$(4+\sqrt{3})(4-\sqrt{3})$

To rationalize the given expression, We need to understand the basic concepts in rationalization of expressions. There are 4 basic expressions to which we can apply any expression.

$(a-b)^2=a^2-2ab+b^2$

$(a+b)^2=a^2+2ab+b^2$

$(a+b)(a-b)=a^2-b^2$

$(x+a)(x+b)=x^2 +(a+b)x+ab$

From these 4 equations we need to find the proper equation which suits the given expression in the question.

We find out that the expression if of the format of the third equation, So we apply the equation.

By applying the equation we get,

$(4 + \sqrt3)(4 - \sqrt3) = 4^2 - \sqrt3^2$

$16 - 3$

$13$

We find that the final answer is equal to 13.

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