Question

How do you simplify the square root of $1.96$ without a calculator?

Answer 1

We can rewrite this expression as:
$\sqrt{1.96}\Rightarrow \sqrt{\frac{100}{100}\times 1.96}\Rightarrow \sqrt{\frac{196}{100}}\Rightarrow \frac{\sqrt{196}}{\sqrt{100}}=\frac{\sqrt{196}}{10}$
Next, we can rewrite the number under the radical as:
$\frac{\sqrt{196}}{10}\Rightarrow \frac{\sqrt{4\times 49}}{10}\Rightarrow \frac{\sqrt{4}\times \sqrt{49}}{10}\Rightarrow \frac{2\times 7}{10}\Rightarrow \frac{14}{10}\Rightarrow 1.4$.