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AlladinOne [14]
4 years ago
11

What is the simplest form of ^3 square root 27a^3b^7

Mathematics
2 answers:
Flura [38]4 years ago
8 0

Answer:

Option (a) is correct.

The simplified form of  \sqrt[3]{27a^3b^7} is 3ab^2\sqrt[3]{b}

Step-by-step explanation:

Given : \sqrt[3]{27a^3b^7}

We have to write the simplest form of given expression \sqrt[3]{27a^3b^7}        

Consider the given expression  \sqrt[3]{27a^3b^7}

27 can be written as 3³

b^7 can be written as b^3b^3b

Thus, expression becomes,

\sqrt[3]{27a^3b^7}=\sqrt[3]{3^3a^3b^6b^3b}

Thus, Simplify, we get,

=3ab^2\sqrt[3]{b}

Thus, The simplified form of  \sqrt[3]{27a^3b^7} is 3ab^2\sqrt[3]{b}

Irina-Kira [14]4 years ago
4 0
\bf \sqrt[3]{27a^3b^7}\quad 
\begin{cases}
27=3\cdot 3\cdot 3\\
\qquad 3^3\\
b^7=b^{3+3+1}\\
\qquad b^3b^3b^1\\
\qquad (b^2)^3b^1
\end{cases}\implies \sqrt[3]{3^3a^3(b^2)^3b^1}
\\\\\\
3ab^2\sqrt[3]{b^1}\implies 3ab^2\sqrt[3]{b}
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