+1904 Rationalize the denominator to these expressions and show how you got your answer
I.) \(\frac{5}{\sqrt{2}}\)
II.) \(\frac{10}{\sqrt[3]{4}}\)
III.) \(\frac{5+\sqrt{2}}{5-\sqrt{2}}\)
IV.) \(\frac{\sqrt{3}}{{tan}^{-1}(\sqrt{3})}\)
V.) \(\frac{3}{\frac{\sqrt[5]{6}}{\sqrt[7]{6}}}\)
+128570 I) 5/ √2 multiply top/bottom by √2 = 5√2 / [√2 * √2] = [5√2] / 2
II) 10/ ∛4 multiply top/bottom by 42/3 = 10 * 42/3 / 4 = [ 5 * 42/3 ] / 2
III) [ 5 + √2] / [ 5 - √2] multiply top/bottom by [5 + √2]
([5 + √2] [ 5 + √2]) / [ 25 - 2] = [25 + 10√2 + 2] / 23 = [ 27 + 10√2] / 23
IV) √3 / arctan (√3) = √3 / [pi/ 3] = [3 √3] / pi
V) 3 / [ 61/5 / 61/7 ] = [3 * 6 1/7 ] / 61/5 multilply top/bottom by 64/5 =
[ 3 * 61/7 * 64/5] / [61/5 * 64/5] = [ 3 * 633/35] / [ 6] = 633/35 / 2
