Question

(Root of 3+root of 5)(root of 12-root of 5root of 15

Answer 1

Answer:

$6-15\sqrt{5}+\sqrt{60}-25\sqrt{3}$

Step-by-step explanation:

$(\sqrt{3}+\sqrt{5})(\sqrt{12}-5\sqrt{15})$

$=\sqrt{3}(\sqrt{12}-5\sqrt{15})+\sqrt{5}(\sqrt{12}-5\sqrt{15})$

$=\sqrt{3}\times 2\sqrt{3}-\sqrt{3}\times 5\sqrt{5\times 3}\\+\sqrt{5}\times \sqrt{12}-\sqrt{5}\times5\sqrt{15}$

$=6-15\sqrt{5}+\sqrt{60}-25\sqrt{3}$

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Answer 2

6  + $2\sqrt{15}$ - 15 $\sqrt{5}$ -  25$\sqrt{3}$

Step-by-step explanation:

Given,

$(\sqrt{3} + \sqrt{5}) (\sqrt{12} - 5\sqrt{15})$

$\\(\sqrt{3} + \sqrt{5}) (2\sqrt{3} - 5\sqrt{15})$

Multiplying:

($\sqrt{3}$ × $2\sqrt{3}$) + ($\sqrt{5}$ × $2\sqrt{3}$) - ($\sqrt{3}$ × $5\sqrt{15}$) - ($\sqrt{5}$ × $5\sqrt{15}$)

Removing the square root from the perfect squares:

(3 × 2) + ( $2\sqrt{15}$) - ($\sqrt{3}$ × $5\sqrt{3 * 5}$) - ($\sqrt{5}$ × $5\sqrt{3 * 5}$)

(6)  + ( $2\sqrt{15}$) - (3 × 5 $\sqrt{5}$) - (5 × 5$\sqrt{3}$)

(6)  + ( $2\sqrt{15}$) - (15 $\sqrt{5}$) - (25$\sqrt{3}$)

6  + $2\sqrt{15}$ - 15 $\sqrt{5}$ -  25$\sqrt{3}$

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