Because $\sqrt{1849}$ = 43, find the value of :

(i) $\sqrt{0.1849}$ + $\sqrt{18.49}$

(ii) $\sqrt{184900}$ - $\sqrt{4 \times 18.49}$

(i)

$\sqrt{0.1849} + \sqrt{18.49}\\[1em] = \sqrt{\dfrac{1849}{10000}} + \sqrt{\dfrac{1849}{100}}\\[1em] = \dfrac{\sqrt{1849}}{\sqrt{10000}} + \dfrac{\sqrt{1849}}{\sqrt{100}}\\[1em] = \dfrac{43}{100} + \dfrac{43}{10}\\[1em] = 0.43 + 4.3\\[1em] = 4.73$

Hence, $\sqrt{0.1849} + \sqrt{18.49} = 4.73$

(ii)

$\sqrt{184900} - \sqrt{4 \times 18.49}\\[1em] = \sqrt{1849 \times 100} - \sqrt{4 \times \dfrac{1849}{100}}\\[1em] = {\sqrt{1849} \times \sqrt{100}} - \sqrt{4} \times \sqrt{\dfrac{1849}{100}}\\[1em] = {43 \times 10} - 2 \times {\dfrac{43}{10}}\\[1em] = 430 - 2 \times 4.3\\[1em] = 430 - 8.6\\[1em] = 421.4$

Hence, $\sqrt{184900} - \sqrt{4 \times 18.49} = 421.4$