Question

\(c\sqrt{20}-\sqrt{45}+3\sqrt{8}+\sqrt{72}\) 

\(d.\dfrac{3}{\sqrt{3}+1}\) 

\(f.\dfrac{2}{\sqrt{10}+\sqrt{7}}\)

Answer 1

c) \(\sqrt{20}-\sqrt{45}+3\sqrt{8}+\sqrt{72}\)

\(=2\sqrt{5}-3\sqrt{5}+6\sqrt{2}+6\sqrt{2}\)

\(=-\sqrt{5}+12\sqrt{2}\)

d) \(\dfrac{3}{\sqrt{3}+1}\)

\(=\dfrac{3\left(\sqrt{3}-1\right)}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}\)

\(=\dfrac{3\left(\sqrt{3}-1\right)}{2}\)

\(=\dfrac{3\sqrt{3}-3}{2}\)

e) \(\dfrac{2}{\sqrt{10}-\sqrt{7}}\)

\(=\dfrac{2\left(\sqrt{10}+\sqrt{7}\right)}{\left(\sqrt{10}-\sqrt{7}\right)\left(\sqrt{10}+\sqrt{7}\right)}\)

\(=\dfrac{2\left(\sqrt{10}+\sqrt{7}\right)}{3}\)

\(=\dfrac{2\sqrt{10}+2\sqrt{7}}{3}\)

Answer 2

c)

\(=\sqrt{4.5}-\sqrt{9.5}+\sqrt{8.9}+\sqrt{72}\\ =2\sqrt{5}-3\sqrt{5}+\sqrt{72}+\sqrt{72}\\ =-\sqrt{5}+2\sqrt{72}\\ =-\sqrt{5}+2\sqrt{36.2}\\ =-\sqrt{5}+12\sqrt{2}\)