Question

Square root of 648.7209 by division method

Answer 1

Answer:

$25.47$

Step-by-step explanation:

This root can be rewritten as:

$\sqrt{\frac{6487209}{10000} }$

$\sqrt{\frac{6487209}{100^{2}} }$

$\frac{1}{100}\cdot \sqrt{6487209}$

Since 6487209 is a multple of 3, the expression can be rearranged as follows:

$\frac{1}{100}\cdot \sqrt{3\times 2162403}$

2162403 is also a multiple of 3, then:

$\frac{1}{100}\cdot \sqrt{3^{2}\times 720801}$

$\frac{3}{100}\cdot \sqrt{720801}$

720801 is a multiple of 3, then:

$\frac{3}{100}\cdot \sqrt{3\times 240267}$

240267 is a multiple of 3, then:

$\frac{3}{100}\times \sqrt{3^{2}\times 80089}$

$\frac{9}{100}\cdot \sqrt{80089}$

80089 is a multiple of 283, then:

$\frac{9}{100}\cdot \sqrt{283^{2}}$

$\frac{9\times 283}{100}$

$\frac{2547}{100}$

$25.47$