Question

(5 - √2) (2 - √5) =

A) 7 - √7
B) 7 + √7
C) 10 - 5 √5 - 2 √2 - √10
D) 10 - 5 √5 - 2 √2 + √10

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Here, We can apply Identity of ( a - b )( c - d ) = ac - ad - bc + bd

Where, a = 5 , b = √2 , c = 2 , d = √5

So,

$\longrightarrow \sf ( 5 -\sqrt{2} ) ( 2 - \sqrt{5} )$

$\longrightarrow \sf (5)(2) - (5)(\sqrt{5}) - (\sqrt{2})(2) + ( \sqrt{2}) (\sqrt{5})$

$\longrightarrow \underline{\boxed{\sf 10 - 5\sqrt{5} - 2\sqrt{2} + \sqrt{10}}}$

Hence, Option (D) is right ✔️

I hope it helps you ❤️✔️