Question

Find the value of $\frac{\sqrt{150.0625}+\sqrt{84.8241}}{\sqrt{59.29}-\sqrt{5.29}}$

Answer 1

$\frac{\sqrt{150.0625}+\sqrt{84.8241}}{\sqrt{59.29}-\sqrt{5.29}}$

$=\frac{\sqrt{\frac{1500625}{10000}}+\sqrt{\frac{848241}{10000}}}{\sqrt{\frac{5929}{100}}-\sqrt{\frac{529}{100}}}$

$=\frac{\sqrt{\frac{35\times 35\times 35\times 35}{10\times 10\times 10\times 10}}+\sqrt{\frac{307\times 3\times 307\times 3}{10\times 10\times 10\times 10}}}{\sqrt{\frac{7\times 7\times 11\times 11}{10\times 10}}-\sqrt{\frac{23\times 23}{10\times 10}}}$

$=\frac{\frac{35\times 35}{10\times 10}+\frac{307\times 3}{10\times 10}}{\frac{7\times 11}{10}-\frac{23}{10}}$

$=\frac{12.25+9.21}{7.7+2.3}=\frac{21.46}{10}=2.146$