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

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Roots of integers

Full solution

Q.

(3-\sqrt{5})(3+\sqrt{5})

Apply difference of squares formula: We will use the difference of squares formula, which states that $(a - b)(a + b) = a^2 - b^2$ , where $a$ and $b$ are any real numbers. In this case, $a$ is $3$ and $b$ is $\sqrt{5}$ .
Calculate $a^2$ : Calculate $a^2$ : $3^2 = 9$ .
Calculate $b^2$ : Calculate $b^2$ : $(\sqrt{5})^2 = 5$ .
Subtract $b^2$ from $a^2$ : Subtract $b^2$ from $a^2$ : $9 - 5 = 4$ .
Find the product: The product of $(3-\sqrt{5})(3+\sqrt{5})$ is therefore $4$ .

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