Question

Transports external factors under the root sign: pls help

Answer 1

See explanation

Explanation:

Use facts

`a=√(a^2)\ [\text{for all} \ a\ge 0]\\ \\a=\sqrt[n]{a^n}\ [\text{for all} \ a\ge 0]`

Hence,

`2√(2)=√(4)\cdot √(2)=√(4\cdot 2)=√(8)\\ \\3√(2)=√(9)\cdot √(2)=√(9\cdot 2)=√(18)\\ \\5√(3)=√(25)\cdot √(3)=√(25\cdot 3)=√(75)\\ \\(1)/(3)√(6)=\sqrt{(1)/(9)}\cdot √(6)=\sqrt{(1)/(9)\cdot 6}=\sqrt{(2)/(3)}\\ \\(3)/(5)√(5)=\sqrt{(9)/(25)}\cdot √(5)=\sqrt{(9)/(25)\cdot 5}=\sqrt{(9)/(5)}\\ \\3\sqrt[3]{3}=\sqrt[3]{27}\cdot \sqrt[3]{3}=\sqrt[3]{27\cdot 3}=\sqrt[3]{81}`

`8√(2)=√(64)\cdot √(2)=√(64\cdot 2)=√(128)\\ \\5\sqrt[5]{3}=\sqrt[5]{5^5}\cdot \sqrt[5]{3}=\sqrt[5]{5^5\cdot 3}=\sqrt[5]{9,375}\\ \\(4)/(3)√(3)=\sqrt{(16)/(9)}\cdot √(3)=\sqrt{(16)/(9)\cdot 3}=\sqrt{(16)/(3)}\\ \\2\sqrt{(1)/(2)}=√(4)\cdot \sqrt{(1)/(2)}=\sqrt{4\cdot (1)/(2)}=√(2)`