What is the value obtained when we expand 1-22 -

The correct option is C 3+2√(2) (1 + √(2))^2 Comparing with nbsp;(a + b)^2, we get a = 1,b = √(()2) Using (a+b)^2 = a^2+2ab+b^2, we get (1 + √(2))^2 nbsp;= ...

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Standard IX

Mathematics

Addition and Subtraction of Like and Unlike Surds

What is the v...

Question

What is the value obtained when we expand $({1 + \sqrt{2})}^{2}$ ?

$2 + 2 \sqrt{2}$

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$3 + 2 \sqrt{2}$

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$3 + 3 \sqrt{2}$

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Solution

The correct option is C
$3 + 2 \sqrt{2}$

${(1 + \sqrt{2})}^{2}$

Comparing with ${(a + b)}^{2}$ , we get a = 1,b = $\sqrt{(} 2)$

Using $(a + b)^{2} = a^{2} + 2 a b + b^{2}$ , we get

${(1 + \sqrt{2})}^{2} = 1 + 2 \sqrt{2} + 2 = 3 + 2 \sqrt{2}$

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What is the value obtained when we expand (1+√2)2?

The correct option is C 3+2√2 (1+√2)2 Comparing with (a+b)2, we get a = 1,b = √(2) Using (a+b)2=a2+2ab+b2, we get (1+√2)2=1+2√2+2=3+2√2

What is the value obtained when we expand $({1 + \sqrt{2})}^{2}$ ?

The correct option is C
$3 + 2 \sqrt{2}$

${(1 + \sqrt{2})}^{2}$

Comparing with ${(a + b)}^{2}$ , we get a = 1,b = $\sqrt{(} 2)$

Using $(a + b)^{2} = a^{2} + 2 a b + b^{2}$ , we get

${(1 + \sqrt{2})}^{2} = 1 + 2 \sqrt{2} + 2 = 3 + 2 \sqrt{2}$