Question

given root 2 is equal to 1.414 and root 6 is equal to 2.449 find the value of 1 by root 3 minus root 2-1 correct to 3 places of decimal.

Answer 1

Answer:

$Value \:of \: \frac{1}{\sqrt{3}-\sqrt{2}-1}≈-1.466$

Step-by-step explanation:

$Given\: \sqrt{2}=1.414,\\\sqrt{6}=2.446$

$Value \:of \: \frac{1}{\sqrt{3}-\sqrt{2}-1}\\=\frac{1}{\sqrt{3}-(\sqrt{2}+1)}\\=\frac{\sqrt{3}+\sqrt{2}+1}{[\sqrt{3}-(\sqrt{2}+1)][\sqrt{3}+(\sqrt({2}+1)]}$$=\frac{\sqrt{3}+\sqrt{2}+1}{(\sqrt{3})^{2}-(\sqrt{2}+1)^{2}}$

$=\frac{\sqrt{3}+\sqrt{2}+1}{3-(2+1+2\times \sqrt{2}}\\=\frac{\sqrt{3}+\sqrt{2}+1}{3-3-2\times \sqrt{2}}\\=\frac{\sqrt{3}+\sqrt{2}+1}{-2\times \sqrt{2}}\\=\frac{\sqrt{2}(\sqrt{3}+\sqrt{2}+1)}{-2\times \sqrt{2}\times \sqrt{2}}\\=\frac{\sqrt{6}+2+\sqrt{2}}{-2\times 2}$

$=\frac{2.449+2+1.414}{-4}\\=\frac{5.863}{-4}\\=\frac{25\times 5.863}{-25\times 4}\\=-\frac{146.575}{100}\\=-1.46575\\≈-1.466$

Therefore,

$Value \:of \: \frac{1}{\sqrt{3}-\sqrt{2}-1}≈-1.466$

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Answer 2

Answer:

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