Which among the following numbers is the greatest ?\(\sqrt[3]{4},\sqrt

1.	Which among the following numbers is the greatest ?\(\sqrt[3]{4},\sqrt{2},\sqrt[6]{16},\sqrt[4]{5}\)
Answer» LCM of (3, 6, 4) = 12, Raising each given number to power 12, ∴ \(\sqrt[3]{4}=\) (4)^{\(\frac{1}{3}\)} = (4^{\(\frac{1}{3}\)} )¹²= 4⁴= 256 \(\sqrt{2}=\) (2)^{^{\(\frac{1}{2}\)}} = (2^{\(\frac{1}{2}\)} )¹²= 4⁶= 64 \(\sqrt[6]{13}=\) (13)^{^{\(\frac{1}{6}\)}} = (13^{\(\frac{1}{6}\)} )¹²= 13²= 169 \(\sqrt[4]{5}=\) (5)^{^{\(\frac{1}{4}\)}} = (4^{\(\frac{1}{4}\)} )¹²= 5³= 125 ⇒ \(\sqrt[3]{4}\) is the greatest.

Which among the following numbers is the greatest ?\(\sqrt[3]{4},\sqrt{2},\sqrt[6]{16},\sqrt[4]{5}\)

Answer»

LCM of (3, 6, 4) = 12, Raising each given number to power 12,

∴ \(\sqrt[3]{4}=\) (4)^{\(\frac{1}{3}\)} = (4^{\(\frac{1}{3}\)} )¹²= 4⁴= 256

\(\sqrt{2}=\) (2)^{^{\(\frac{1}{2}\)}} = (2^{\(\frac{1}{2}\)} )¹²= 4⁶= 64

\(\sqrt[6]{13}=\) (13)^{^{\(\frac{1}{6}\)}} = (13^{\(\frac{1}{6}\)} )¹²= 13²= 169

\(\sqrt[4]{5}=\) (5)^{^{\(\frac{1}{4}\)}} = (4^{\(\frac{1}{4}\)} )¹²= 5³= 125

⇒ \(\sqrt[3]{4}\) is the greatest.