Find the value of -3-72- Is it rational- -4 MARKS-

Concept : 1 Mark Calculation : 2 Marks Identification : 1 Mark We have, (√(3)+√(7))^2=(√(3))^2+(√(7))^2+2×√(3)×√(7)= 3 + 7 +2√(21) [using the identity (a+b)^2= ...

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Standard IX

Mathematics

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Find the valu...

Question

Find the value of ${(\sqrt{3} + \sqrt{7})}^{2}$ . Is it rational? [4 MARKS]

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Solution

Concept : 1 Mark
Calculation : 2 Marks
Identification : 1 Mark
We have,

${(\sqrt{3} + \sqrt{7})}^{2} = (\sqrt{3})^{2} + (\sqrt{7})^{2} + 2 \times \sqrt{3} \times \sqrt{7} = 3 + 7 + 2 \sqrt{21}$
$[u s i n g t h e i d e n t i t y {(a + b)}^{2}$ = $a^{2} + b^{2} + 2 a b]$

The result is an irrational number.

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Find the value of (√3+√7)2. Is it rational? [4 MARKS]

Concept : 1 Mark Calculation : 2 Marks Identification : 1 Mark We have, (√3+√7)2=(√3)2+(√7)2+2×√3×√7=3+7+2√21 [using the identity (a+b)2= a2+b2+2ab] The result is an irrational number.

Find the value of ${(\sqrt{3} + \sqrt{7})}^{2}$ . Is it rational? [4 MARKS]