Question

answer the question ​

Answer 1

Answer:

on solving √8+√2√15 answere will come 8.3

on solving d 5+√3 we get answere releated to it

so d is option

Answer 2

Given Question :-

$\rm :\longmapsto\: \sqrt{8 + 2 \sqrt{15} } = - - - - -$

$\: \: \: \: \: (a) \: \: \sqrt{5} + \sqrt{3}$

$\: \: \: \: \: (b) \: \: \sqrt{5} - \sqrt{3}$

$\: \: \: \: \: (c) \: \: \sqrt{5} + 3$

$\: \: \: \: \: (d) \: \: \sqrt{3} + 5$

$\red{\large\underline{\sf{Solution-}}}$

Given expression is

$\rm :\longmapsto\: \sqrt{8 + 2 \sqrt{15} }$

can be rewritten as

$\rm \:  =  \: \sqrt{5 + 3 + 2 \sqrt{5 \times 3} }$

can further rewritten as

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

We know,

$\rm :\longmapsto\:\boxed{ \tt{ \: {x}^{2} + {y}^{2} + 2xy = {(x + y)}^{2} \: }}$

So, using this identity, we get

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

$\rm \:  =  \: \sqrt{5} + \sqrt{3}$

Hence,

$\rm \implies\:\boxed{ \tt{ \: \sqrt{8 + 2 \sqrt{15}} = \sqrt{5} + \sqrt{3} \: }}$

• So, option (a) is correct.

More Identities to know :-

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

a² - b² = (a + b)(a - b)

(a + b)² = (a - b)² + 4ab

(a - b)² = (a + b)² - 4ab

(a + b)² + (a - b)² = 2(a² + b²)

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)³ = a³ - b³ - 3ab(a - b)