Question

(root3+root11)square + (root3-root11)square

Answer 1

Answer:

28

Step-by-step explanation:

Here, we are asked to expand the following the expression:

$\longrightarrow \sf{\quad { { \Big ( \sqrt{3} + \sqrt{11} \Big)}^2+ { \Big ( \sqrt{3} - \sqrt{11} \Big)}^2 }}$

Basically, we need to apply algebraic identities to tackle this question. As we know that, (a + b)² is equivalent to a² + b² + 2ab and (a – b)² is equivalent to a² + b² – 2ab. Same goes with the terms of the given expression.

$\longrightarrow \sf{\quad {\Big \{ (\sqrt{3})^2 + (\sqrt{11})^2 + 2(\sqrt{3} \times \sqrt{11} ) \Big \} +\Big \{ (\sqrt{3})^2 + (\sqrt{11})^2 - 2(\sqrt{3} \times \sqrt{11}) \Big \}} }$

Simplifying further by performing multiplication and writing the squares of the numbers.

$\longrightarrow \sf{\quad {\Big \{ 3 + 11 + 2(\sqrt{33}) \Big \} +\Big \{ 3 + 11 - 2(\sqrt{33} )\Big \} }}$

Performing multiplication and removing the brackets.

$\longrightarrow \sf{\quad { 14 \cancel{+ 2\sqrt{33}} + 14 \cancel{- 2\sqrt{33}} } }$

Performing addition and subtraction.

$\longrightarrow \quad\underline{\boxed{ \textbf{\textsf{28}} }}$

∴ The required answer is 28.

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

More Identities :

• (√a)² = a

• √a√b = √ab

• √a/√b = √a/b

• (√a + √b)(√a - √b) = a - b

• (a + √b)(a - √b) = a² - b

• (√a ± √b)² = a ± 2√ab + b

• (√a + √b)(√c + √d) = √ac + √ad + √bc + √bd

Answer 2

$\purple{\huge \bf \underline{\underline{Question : }}}$

$\bf {( \sqrt{3} + \sqrt{11} )}^{2} + {( \sqrt{3} - \sqrt{11} )}^{2}$

$\purple{\huge \bf \underline{\underline{Answer: }}}$

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

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

$\implies ({\sqrt{3 })^{2}} + {( \sqrt{11} )}^{2} + 2( \sqrt{3})( \sqrt{11} ) + ({\sqrt{3 })^{2}} + {( \sqrt{11} )}^{2} - 2( \sqrt{3})( \sqrt{11}) \\ \\ \implies3 + 11 + \cancel{ 2 \sqrt{33}} + 3 + 11 - \cancel{2 \sqrt{33}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies28\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$