The value of 3-22 isa 3-2b 3-2c 2-1d 2-1

3 22=2+1 2 #215;2 #215;1=22+12 2 #215;2 #215;1 This is of the form a2+b2 2ab=a b2 22+12 2 #215;2 #215;1=2 12So, #160;3 22=2 12=2 1 Hence, the corr ...

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Standard IV

Mathematics

Multiplication Trick for a Table

The value of ...

Question

The value of $\sqrt{3 - 2 \sqrt{2}}$ is
(a) $\sqrt{3} + \sqrt{2}$
(b) $\sqrt{3} - \sqrt{2}$
(c) $\sqrt{2} + 1$
(d) $\sqrt{2} - 1$

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Solution

$3 - 2 \sqrt{2} = 2 + 1 - 2 \times \sqrt{2} \times 1 = {(\sqrt{2})}^{2} + 1^{2} - 2 \times \sqrt{2} \times 1$
This is of the form
$a^{2} + b^{2} - 2 a b = {(a - b)}^{2}$
${(\sqrt{2})}^{2} + 1^{2} - 2 \times \sqrt{2} \times 1 = {((\sqrt{2}) - 1)}^{2} So, \sqrt{3 - 2 \sqrt{2}} = \sqrt{{((\sqrt{2}) - 1)}^{2}} = \sqrt{2} - 1$
Hence, the correct answer is option (d).

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The value of 3-22 is (a) 3+2 (b) 3-2 (c) 2+1 (d) 2-1

3-22=2+1-2×2×1=22+12-2×2×1 This is of the form a2+b2-2ab=a-b2 22+12-2×2×1=2-12So, 3-22=2-12=2-1 Hence, the correct answer is option (d).

The value of $\sqrt{3 - 2 \sqrt{2}}$ is
(a) $\sqrt{3} + \sqrt{2}$
(b) $\sqrt{3} - \sqrt{2}$
(c) $\sqrt{2} + 1$
(d) $\sqrt{2} - 1$