Question

Find the value of 9^3/2 -3 x 5⁰- (1/18)^-1/2

Answer 1

We are given

$$\begin{gathered} 9^{\frac{3}{2}}-3\times 5^0-{\left(\frac{1}{18}\right)}^{\frac{-1}{2}} \\ ={\left(3^2\right)}^{\frac{3}{2}}-3\times 5^0-{\left(\frac{1}{18}\right)}^{\frac{-1}{2}} \\ =3^3-3\times 1-{\left(18\right)}^{\frac{1}{2}},\mathrm{we}\mathrm{know}{a}^0=1 \\ =27-3-{\left(3^2\times 2\right)}^{\frac{1}{2}} \\ =24-\left(3^{2\times \frac{1}{2}}\times 2^{\frac{1}{2}}\right) \\ =24-\left(3\times \sqrt{2}\right) \\ =3(8-\sqrt{2})\left(\mathrm{answer}\right) \end{gathered}$$