Question

Simplify the following using multiplication and division properties of surds root 225/729 - root 25/144 ÷ root 16 / 81

Answer 1

Answer:

Simplify the following using multiplication and division properties of surds:

$\sqrt\frac{225}{729}$ - $\sqrt\frac{25}{144}$ ÷ $\sqrt\frac{16}{81}$

= $\frac{-55}{144}$

Explanation:

To solve the following equation by use of the multiplication and division of surds, we will use the second property of surds:

$\sqrt\frac{225}{729}$ - $\sqrt\frac{25}{144}$ ÷ $\sqrt\frac{16}{81}$

Second multiplication property of surds:

$\sqrt\frac{a}{b}$  can be written as or = $\frac{\sqrt{a} }{\sqrt{b} }$

Therefore:

$\sqrt\frac{225}{729}$ - $\sqrt\frac{25}{144}$ ÷ $\sqrt\frac{16}{81}$   =  $\frac{\sqrt{225} }{\sqrt{729} }$ - $\frac{\sqrt{25} }{\sqrt{144} }$ ÷ $\frac{\sqrt{16} }{\sqrt{81} }$

= $\frac{15}{27}$ - $\frac{5}{12}$ ÷ $\frac{4}{9}$

At this point, you will use PEMDAS/BODMAS to solve equation.

First start with the divison then subtraction:

Division

$\frac{15}{27}$ - $\frac{5}{12}$ ÷ $\frac{4}{9}$

$\frac{15}{27}$ - $\frac{5}{12}$ ÷ $\frac{4}{9}$

$\frac{5}{12}$ ÷ $\frac{4}{9}$ = $\frac{5}{12}$ × $\frac{9}{4}$  = $\frac{15}{16}$

Subtraction:

$\frac{15}{27}$ - $\frac{15}{16}$

= $\frac{240 - 405}{432}$

= $\frac{-165}{432}$

= $\frac{-55}{144}$

The solution to this thus = $\frac{-55}{144}$