Question

\(\frac{\sqrt{12,5}}{\sqrt{0,5}}\)

\(\frac{\sqrt{6}}{\sqrt{150}}\)

\(\sqrt{6,8^2-3,2^2}\)

\(\sqrt{21,8^2-18,2^2}\)

Answer 1

\(\frac{\sqrt{12,5}}{\sqrt{0,5}}=\frac{\sqrt{0,5}.\sqrt{25}}{\sqrt{0,5}}=\sqrt{25}=5\)

\(\frac{\sqrt{6}}{\sqrt{150}}=\frac{\sqrt{6}}{\sqrt{6}.\sqrt{25}}=\frac{1}{\sqrt{25}}=\frac{1}{5}\)

\(\sqrt{6,8^2-3,2^2}=\sqrt{\left(6,8+3,2\right)\left(6,8-3,2\right)}=\sqrt{10.3,6}=\sqrt{36}=6\)

\(\sqrt{21,8^2-18,2^2}=\sqrt{\left(21,8+18,2\right)\left(21,8-18,2\right)}=\sqrt{40.3,6}=\sqrt{144}=12\)

Answer 2

\(\frac{\sqrt{12,5}}{\sqrt{0,5}}=\sqrt{\frac{12,5}{0,5}}=\sqrt{25}=5\)

\(\frac{\sqrt{6}}{\sqrt{150}}=\sqrt{\frac{6}{150}}=\sqrt{\frac{1}{25}}=\frac{1}{5}\)

\(\sqrt{\left(6,8\right)^2-\left(3,2\right)^2}=\sqrt{46,24-10,24}=\sqrt{36}=6\)

\(\sqrt{\left(21,8\right)^2-\left(18,2\right)^2}=\sqrt{475,24-331,24}=\sqrt{144}=12\)