Simplify the following:
(32−5)13(32+5)13(\sqrt{32} - \sqrt{5})^{\dfrac{1}{3}}(\sqrt{32} + \sqrt{5})^{\dfrac{1}{3}}(32−5)31(32+5)31
28 Likes
Given,
⇒(32−5)13(32+5)13⇒[(32−5)(32+5)]13\Rightarrow (\sqrt{32} - \sqrt{5})^{\dfrac{1}{3}}(\sqrt{32} + \sqrt{5})^{\dfrac{1}{3}} \\[1em] \Rightarrow [(\sqrt{32} - \sqrt{5})(\sqrt{32} + \sqrt{5})]^{\dfrac{1}{3}}⇒(32−5)31(32+5)31⇒[(32−5)(32+5)]31
As (a - b)(a + b) = a2 - b2 we get,
⇒[(32)2−(52)]13⇒[32−5]13⇒(27)13⇒(33)13⇒3.\Rightarrow [(\sqrt{32})^2 - (\sqrt{5}^2)]^{\dfrac{1}{3}} \\[1em] \Rightarrow [32 - 5]^{\dfrac{1}{3}} \\[1em] \Rightarrow (27)^{\dfrac{1}{3}} \\[1em] \Rightarrow (3^3)^{\dfrac{1}{3}} \\[1em] \Rightarrow 3.⇒[(32)2−(52)]31⇒[32−5]31⇒(27)31⇒(33)31⇒3.
Hence, (32−5)13(32+5)13(\sqrt{32} - \sqrt{5})^{\dfrac{1}{3}}(\sqrt{32} + \sqrt{5})^{\dfrac{1}{3}}(32−5)31(32+5)31 = 3.
Answered By
15 Likes
72n+3−(49)n+2((343)n+1)23\dfrac{7^{2n + 3} - (49)^{n + 2}}{((343)^{n + 1})^{\dfrac{2}{3}}}((343)n+1)3272n+3−(49)n+2
(27)43+(32)0.8+(0.8)−1(27)^{\dfrac{4}{3}} + (32)^{0.8} + (0.8)^{-1}(27)34+(32)0.8+(0.8)−1
(x13−x−13)(x23+1+x−23)\Big(x^{\dfrac{1}{3}} - x^{-\dfrac{1}{3}}\Big)\Big(x^{\dfrac{2}{3}} + 1 + x^{-\dfrac{2}{3}}\Big)(x31−x−31)(x32+1+x−32)
(xmxn)l.(xnxl)m.(xlxm)n\Big(\dfrac{x^m}{x^n}\Big)^l.\Big(\dfrac{x^n}{x^l}\Big)^m.\Big(\dfrac{x^l}{x^m}\Big)^n(xnxm)l.(xlxn)m.(xmxl)n
