Question

Find the square root of 7 correct to two decimal places; then use it to find the value of

$\sqrt{\frac{4+\sqrt{7}}{4+\sqrt{7}}}$ correct to three significant digits.

Answer 1

$\sqrt{7}=2.645=2.65$

Now, $\sqrt{\frac{4+\sqrt{7}}{4+\sqrt{7}}}$
$\sqrt{\frac{(4+\sqrt{7})(4+\sqrt{7})}{(4-\sqrt{7})(4+\sqrt{7})}}\sqrt{\frac{(4+\sqrt{7}{)}^2}{(4{)}^2-(\sqrt{7}{)}^2}}=\sqrt{\frac{(4+\sqrt{7}{)}^2}{16-7}}=\sqrt{\frac{(4+\sqrt{7}{)}^2}{9}}=\frac{4+\sqrt{7}}{3}=\frac{4+2.65}{3}=\frac{6.65}{3}=2.22$