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

Jun 18, 2018

See a solution process below:

#### Explanation:

We can rewrite this expression as:

$\sqrt{1.96} \implies \sqrt{\frac{100}{100} \times 1.96} \implies \sqrt{\frac{196}{100}} \implies \frac{\sqrt{196}}{\sqrt{100}} = \frac{\sqrt{196}}{10}$

Next, we can rewrite the number under the radical as:

$\frac{\sqrt{196}}{10} \implies \frac{\sqrt{4 \times 49}}{10} \implies \frac{\sqrt{4} \times \sqrt{49}}{10} \implies \frac{2 \times 7}{10} \implies \frac{14}{10} \implies 1.4$