Simplifying Radical Expression $\frac23\sqrt{\frac92}+\frac32\sqrt[3]{16}+\frac14\sqrt{72}$

59 Views Asked by At

Simplify$$\frac23\sqrt{\frac92}+\frac32\sqrt[3]{16}+\frac14\sqrt{72}$$

My try: $$\frac23\cdot\frac3{\sqrt2}+3\sqrt[3]{2}+\frac32\sqrt{2}$$ $$\sqrt2+3\sqrt[3]{2}+\frac32\sqrt{2}$$ $$3\sqrt[3]{2}+\frac52\sqrt{2}$$ Is this correct?