Which of the following real numbers has the maximum value? $$\sqrt{2}, \ \sqrt[3]{3}, \ \sqrt[4]{4}, \ \sqrt{6 \times 5}$$​

Correct option is D

​$$\sqrt{2}, \ \sqrt[3]{3}, \ \sqrt[4]{4}, \ \sqrt{6 \times 5}\\2^\frac{1}{2}, 3^\frac{1}{3}, 4^\frac{1}{4}, 30^\frac{1}{2}\\\text{Take the LCM denominators of powers}\\\text{LCM of 2, 3, 4}= 12 \\2^\frac{12}{2}, 3^\frac{12}{3}, 4^\frac{12}{4}, 30^\frac{12}{2}\\2^6, 3^4, 4^3, 30^6\\2^6 = 64\\3^4= 81\\4^3 = 64\\30^6= 729000000\\$$​​