Simplifying Expressions with Radicals: Product

$\sqrt{24}×\sqrt8×\sqrt3=\sqrt{24×24}=\sqrt{24^2}=\boxed{24}$

√3 x √8 = √24

√24 x √24 = √24² = 24

Since $24, 3, 8$ are non-negative, we can multiply the surds

$\sqrt{24} \times \sqrt{3} \times \sqrt{8} = \sqrt{24 \times 24} = \boxed{24}$

Since $3 \times 8 = { 24}$ , $\sqrt{3} \times \sqrt{8} = \sqrt{ 24}$ . We then get

$\sqrt{ 24 } \times \sqrt{3} \times \sqrt{ 8 } = \sqrt{ 24 } \times \sqrt{ 24 }= \boxed{24}.$

Note that $A$ and $B$ must be non-negative real numbers so that we may apply $\sqrt{A} \times \sqrt{B} = \sqrt{A \times B}$ . Otherwise, we will have to deal with imaginary numbers.