Question

(√3+√7)^
${?}^{2}$
​

Answer 1

Step-by-step explanation:

${( \sqrt{3} + \sqrt{7} )}^{2} = 3 + 7 + 2 \sqrt{21} = 10 + 2 \sqrt{21}$

Answer 2

Question :-

$find \: value \: of \: ({ \sqrt{3} + \sqrt{7} })^{2}$

Required Answer :-

We can see that, on the given question, (a+b)² will satisfy.

and Hence, we can solve this question by using the formula for (a+b)² by supposing a = √3 and b= √7

Now,

Before solving this question, We should solve (a+b)²

=>

( a+b) ² = a² +b² + 2ab

So,

We can solve (√3+√7)² as =>

${( \sqrt{3} + \sqrt{7} )}^{2} - - (using \: ({a + b))}^{2} \\ = > { \sqrt{3} }^{2} + { \sqrt{7} }^{2} + 2 \times \sqrt{3} \times \sqrt{7} \\ = > 3 + 7 + 2 \times \sqrt{21} \\ = > 10 + 2 \sqrt{21}$

Hence, our answer of question (√3+√7)² = 10+2√21

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Some useful algebraic identities are =

• (a+b)² = a² + b² + 2ab

• (a-b)² = a² +b² - 2ab

• a² - b² = (a+b (a-b)

• (a+b) (a+c) = a² + a(a+b) + ab

• (a+b+c)² = a²+b²+c²+2ab+2bc+2ac

• (a+b)³ = a³+b³+3ab(a+b)

• (a-b)³ = a³-b³- 3ab(a-b)

• a³+b³+c³-3abc = (a+b+c) (a²+b²+c²-ab-bc-ca)