Question

√3-2√2=? options are 1+√2 or 1-√2 or √2-1 or √3-√2

Answer 1

$\sqrt{3 - 2 \sqrt{2} }$




Splitting 3 in two numbers so that it could be in the formula of ( a - b )² = a² + b² - 2ab.we have assume 3 as a + b, for this we have to splitting 3 in two numbers.



Possible formation, we can't take negative number because square of any number cant be negative.

3 = 2 + 1




$\sqrt{2 + 1 - 2 \sqrt{2} }$



Now we can compare the identity with our current solution.



$\sqrt{ {( \sqrt{2}) }^{2} + {1}^{2} - 2 (1 \times \sqrt{2}) }$



Convert a² + b² - 2ab in ( a - b )².



$\sqrt{ {( \sqrt{2} + 1) }^{2} } \\ \\ (\sqrt{2} + 1 {)}^{2 \times \frac{1}{2} } \\ \\ \sqrt{2} + 1$




Therefore option A is correct that is 1 + √2