<img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B125%20%7D%20-%20%5Csqrt%7B180%7D%20%2B%20%5Csqrt%7B45%7D%20" id="TexFormula1" tit

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3 years ago

le=" \sqrt{125 } - \sqrt{180} + \sqrt{45} " alt=" \sqrt{125 } - \sqrt{180} + \sqrt{45} " align="absmiddle" class="latex-formula">

Mathematics

1 answer:

Kobotan [32]3 years ago

3 0

Answer:

2 $\sqrt{5}$

Step-by-step explanation:

Using the rule of radicals

$\sqrt{a}$ × $\sqrt{b}$ ⇔ $\sqrt{ab}$

Simplifying the radicals

$\sqrt{125}$ = $\sqrt{25(5)}$ = $\sqrt{25}$ × $\sqrt{5}$ = 5 $\sqrt{5}$

$\sqrt{180}$ = $\sqrt{36(5)}$ = $\sqrt{36}$ × $\sqrt{5}$ = 6 $\sqrt{5}$

$\sqrt{45}$ = $\sqrt{9(5)}$ = $\sqrt{9}$ × $\sqrt{5}$ = 3 $\sqrt{5}$

Thus

$\sqrt{125}$ - $\sqrt{180}$ + $\sqrt{45}$

= 5 $\sqrt{5}$ - 6 $\sqrt{5}$ + 3 $\sqrt{5}$

= 2 $\sqrt{5}$

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