Expand 2-22-Is it rational- -3 MARKS-

Concept : 1 Mark Calculation : 2 Marks By using the identity : nbsp;(a+b)^2 nbsp;= a^2 + 2ab + b^2, We have, nbsp; (2+√(2))^2= 2^2+2×2×√(2)+√(2)^2 = 4+2 ...

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Standard X

Mathematics

Irrational Numbers

Expand 2+√22....

Question

Expand ${(2 + \sqrt{2})}^{2}$ .Is it rational? [3 MARKS]

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Solution

Concept : 1 Mark
Calculation : 2 Marks

By using the identity :
${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$ ,
We have,
${(2 + \sqrt{2})}^{2} = 2^{2} + 2 \times 2 \times \sqrt{2} + {\sqrt{2}}^{2} = 4 + 2 + 4 \sqrt{2} = 6 + 4 \sqrt{2}$

The obtained value contiains a rational and an irrational part. Hence, it is not rational.

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Expand (2+√2)2.Is it rational? [3 MARKS]

Concept : 1 Mark Calculation : 2 Marks By using the identity : (a+b)2=a2+2ab+b2, We have, (2+√2)2=22+2×2×√2+√22=4+2+4√2=6+4√2 The obtained value contiains a rational and an irrational part. Hence, it is not rational.

Expand ${(2 + \sqrt{2})}^{2}$ .Is it rational? [3 MARKS]