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]
