Property 5
In radical expressions, when making rationalizing division, the expression is expanded using the conjugate of the denominator and the denominator is made rational.
\(a\in\mathbb R^+\)
\(\blacksquare\quad\sqrt a\quad\text{(conjugate of)}\quad\sqrt a\qquad\sqrt a\cdot\sqrt a=a\)
\(\blacksquare\quad\sqrt[n]{a}\quad\text{(conjugate of)}\quad\sqrt[n]{a^{n-1}}\qquad\sqrt[n]{a}\cdot\sqrt[n]{a^{n-1}}=a\)
1.
\(\samefrac4{\sqrt2}=?\)
2.
\(\samefrac{10}{\sqrt5}+2\sqrt5=?\)
3.
\(\samefrac6{\sqrt2}+\samefrac4{\sqrt2}=?\)
4.
\(\samefrac4{\sqrt[3]2}=?\)
5.
\(\samefrac5{\sqrt[5]{5^3}}=?\)
6.
\(4\left(3\sqrt2-\samefrac1{\sqrt2}\right)=?\)
7.
\(3\cdot\left(\samefrac{12}{\sqrt3}-\samefrac5{\sqrt3}\right)=?\)
8.
\(1-\samefrac1{\sqrt2}=?\)
9.
\(1-\samefrac1{\sqrt3}=?\)
10.
\(\samefrac{30}{\sqrt5}-\samefrac{15}{\sqrt5}+3\sqrt5=?\)
11.
\(\left(\samefrac5{\sqrt2}+\samefrac7{\sqrt2}\right)\cdot2=?\)
12.
\(\left(4\sqrt3-\samefrac6{\sqrt3}\right)\cdot5=?\)
13.
\(\left(\samefrac4{\sqrt2}-\samefrac3{\sqrt2}\right)\cdot\left(\samefrac6{\sqrt3}\right)=?\)
14.
\(\left(\samefrac{12}{\sqrt3}-\samefrac5{\sqrt3}\right)\cdot\samefrac1{\sqrt7}=?\)
15.
\(\left(\samefrac9{\sqrt3}-\sqrt3\right)\cdot\samefrac1{\sqrt2}=?\)