Question

(√3+√2)^ 2

Please answer this ​

Answer 1

Answer :

↪ 5 + 2√6

Step-by-step explanation :

↪ (√3 + √2)²

• [ (a+b)² = a² + b² + 2ab ]

Here, a = √3 and b = √2, so:

↠ (√3)² + (√2)² + 2(√3)(√2)

↠ 3 + 2 + 2 (√6)

↠ 5 + 2√6

Therefore we can conclude,

(√3 + √2)² = 5 + 2√6

Extra information :-

↪ In the Given question ; √3 and √2 are numbers . Generally we called it as irrational numbers .

√3 = 1.7320508076

√2 = 1.41412135624

↪ The irrational numbers are all the real numbers which are not rational numbers.

Identities :-

↪ (a+b)² = a² + b² + 2ab

↪ (a-b)² = a² + b² - 2ab

↪ (a+b)³ = a³ + 3a²b + 3ab² + b³

↪ (a-b)³ = a³ - 3a²b + 3ab² - b³

Answer 2

Answer:

$\large 5+2\sqrt{6}$

Step-by-step explanation:

$\large (\sqrt{3} +\sqrt{2} )^2\\\\\\\large Using \ identity \ (a+b)^2=a^2+b^2+2ab\\\\\\\large \text{Here a=\sqrt{3} \ and \ b=\sqrt{2} }\\\\\\\large \text{ (\sqrt{3} +\sqrt{2} )^2 = (\sqrt{3})^2+(\sqrt{2})^2+2\times\sqrt{3}\times\sqrt{2} }$

$\large (\sqrt{3} +\sqrt{2} )^2=3+2+2\sqrt{6}\\\\\\\large (\sqrt{3} +\sqrt{2} )^2=5+2\sqrt{6}$

$\large \text{Some important identity that you should have known}\\\\\\\large (x-y )^2= x^2+y^2-2xy\\\\\\\large (x+y )^3= x^3+y^3+3xy(x+y)\\\\\\\large (x-y)^3= x^3-y^3-3xy(x-y)\\\\\\\large (x+y+z )^2= x^2+y^2+z^2+2(xy+yz+xz)$