what is the simplest form of $sqrt3{27a^{3}b^{7}}$?\n$3ab^{2}(sqrt3{b})$\n$3ab^{3}(sqrt3{3ab})$\n$9ab^{2}(sqr…
what is the simplest form of $sqrt3{27a^{3}b^{7}}$?\n$3ab^{2}(sqrt3{b})$\n$3ab^{3}(sqrt3{3ab})$\n$9ab^{2}(sqrt3{b})$\n$9ab^{3}(sqrt3{3ab})$
Answer
Explanation:
Step1: Break - down the components
We know that $\sqrt[3]{27a^{3}b^{7}}=\sqrt[3]{27}\times\sqrt[3]{a^{3}}\times\sqrt[3]{b^{7}}$. Since $\sqrt[3]{27} = 3$, $\sqrt[3]{a^{3}}=a$.
Step2: Simplify $\sqrt[3]{b^{7}}$
We can write $b^{7}=b^{6}\times b$. Then $\sqrt[3]{b^{7}}=\sqrt[3]{b^{6}\times b}=\sqrt[3]{b^{6}}\times\sqrt[3]{b}=b^{2}\sqrt[3]{b}$.
Step3: Combine the results
$\sqrt[3]{27a^{3}b^{7}} = 3\times a\times b^{2}\sqrt[3]{b}=3ab^{2}\sqrt[3]{b}$.
Answer:
$3ab^{2}(\sqrt[3]{b})$