Question

simplyfy (root2 + root5)^2

Answer 1

$\huge\underline{\mathfrak{Question}}$

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

$\huge\boxed{\mathfrak{Answer}}$

As, in this question Root is over the two numbers, and if we double it that is square it, the roots will be removed....and 2 will be multiplied by √5 and √2.

THE SOLUTION IS GIVEN BELOW

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

Solving it on the Formula $\\ (a+b)^{2} = a^{2}+2a \times b+b^ {2}$

⟹ $(\sqrt{2} ) ^ {2} + 2 \times \sqrt{2} \times \sqrt{5} + ( \sqrt{5})^{2}$

⟹ $2 + 2 \sqrt{10} + 5$

⟹ $7 + 2 \sqrt{10}$

$\boxed{\red{7+2 \sqrt{10}}}$

Some of The Important Identities are :-

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

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

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

$(a+b)^{3} = a^{3} +3a^{2}b + 3a b^{2} + b^{3}$

$(a-b)^{3} = a^{3} -3a^{2}b + 3a b^{2} - b^{3}$

Answer 2

Question :–

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

ANSWER :–

$\\ \longrightarrow { \boxed{ \bold { {( \sqrt{2} + \sqrt{5} )}^{2} = 7 + 2 \sqrt{10} }}}$

EXPLANATION :–

• We know that –

$\\ \implies{ \red{ \boxed{ \bold {{( a + b) }^{2} = {a}^{2} + {b}^{2} + 2ab }}}}$

• Now Applying formula –

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

$\\ { \bold { \: \: \: \: \: \: \: \: \: \: \: \: = 2 + 5 + 2 \sqrt{10} }}$

$\\ { \bold { \: \: \: \: \: \: \: \: \: \: \: \: = 7 + 2 \sqrt{10} }}$

Hence , ${ \boxed{ \bold { {( \sqrt{2} + \sqrt{5} )}^{2} = 7 + 2 \sqrt{10} }}}$

Important formula :–

$\\ { \pink{ \bold { (1) \: \: {( a + b )}^{2} = {a}^{2} + {b}^{2} + 2ab }}}$

$\\ { \pink{ \bold { (2) \: \: {( a - b )}^{2} = {a}^{2} + {b}^{2} - 2ab }}}$

$\\ { \pink{ \bold { (3) \: \: {( a + b )}^{3} = {a}^{3} + {b}^{3} + 3ab (a + b)}}}$

$\\ { \pink{ \bold { (4) \: \: {( a - b )}^{3} = {a}^{3} - {b}^{3} - 3ab (a - b)}}}$