Question

simplify each of the following expression: I) (√5+√2) power 2 ii) (√5-√2) (√5+√2)​

Answer 1

Step-by-step explanation:

((√5)² - ( √2)²)

= 5- 2

= 3

Answer 2

$\huge\mathbb{\green{answer}}$

☆By using ALGEBRAIC IDENTITY ☆

${(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab$

$1 \: {( \sqrt{5} + \sqrt{2} ) }^{2}$

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

$= 5 + 3 + \sqrt[2]{15}$

$= 8 + \sqrt[2]{15}$

The required ANSWER is 8+2root 15

Now,

${a}^{2} - {b}^{2} = (a + b)(a - b)$

$2 \: ( \sqrt{5} - \sqrt{2} )( \sqrt{5} + \sqrt{2} )$

$= { \sqrt{5} }^{2} - { \sqrt{2} }^{2}$

$=5 - 2$

$= 3$

The required ANSWER is 3