Question

multiply the radical expression. express numb
$(sqrt{35a^{2}b})(sqrt{5ab^{2}})=square$

Explanation:

Step1: Use product - rule of radicals

$\sqrt{35a^{2}b}\times\sqrt{5ab^{2}}=\sqrt{35a^{2}b\times5ab^{2}}$

Step2: Multiply the coefficients and add exponents of like - bases

$35\times5 = 175$, and for the variables: $a^{2}\times a=a^{2 + 1}=a^{3}$, $b\times b^{2}=b^{1+2}=b^{3}$. So we have $\sqrt{175a^{3}b^{3}}$

Step3: Simplify the radical

$175=25\times7$, $a^{3}=a^{2}\times a$, $b^{3}=b^{2}\times b$. Then $\sqrt{175a^{3}b^{3}}=\sqrt{25\times7\times a^{2}\times a\times b^{2}\times b}=5ab\sqrt{7ab}$

Answer:

$5ab\sqrt{7ab}$