which of the following is equal to square root 50a^6b^7?

Answer:[tex]5\sqrt{2}a^3b^{\frac{7}{2}}}.[/tex]Step-by-step explanation:We need to calculate [tex]\sqrt{50a^6b^7}[/tex]. The properties of radicals say that a root of a product is a product of roots, i.e we can separate the root to each factor:[tex]\sqrt{50a^6b^7}=\sqrt{50}\sqrt{a^6}\sqrt{b^7}.[/tex]Now, another property of radicals says that if there is a root of one term with exponent, the result will be the term to the exponent divided by the root index, that is[tex]\sqrt{50}\sqrt{a^6}\sqrt{b^7}= \sqrt{50}a^{\frac{6}{2}}b^{\frac{7}{2}}= \sqrt{50}a^3b^{\frac{7}{2}}}.[/tex]Finally, we can change the 50 to 25*2 to simplify:[tex]\sqrt{50}a^3b^{\frac{7}{2}}}= \sqrt{25*2}a^3b^{\frac{7}{2}}} =\sqrt{25}\sqrt{2}a^3b^{\frac{7}{2}}} = 5\sqrt{2}a^3b^{\frac{7}{2}}}.[/tex]