Question

question
assuming x and y are both positive, write the following expression in simplest radical form.
\sqrt{36x^{3}y^{7}}
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Explanation:

Step1: Factor the radicand

We can factor the expression inside the square root as follows:
\(36x^{3}y^{7}=36\times x^{2}\times x\times y^{6}\times y\)

Step2: Apply the square root property

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\) and \(b\) are non - negative), we have:
\(\sqrt{36x^{3}y^{7}}=\sqrt{36}\times\sqrt{x^{2}}\times\sqrt{x}\times\sqrt{y^{6}}\times\sqrt{y}\)
We know that \(\sqrt{36} = 6\), \(\sqrt{x^{2}}=x\) (since \(x>0\)) and \(\sqrt{y^{6}}=y^{3}\) (since \(y > 0\)).
Substituting these values in, we get:
\(6\times x\times y^{3}\times\sqrt{x\times y}\)
Simplifying the expression, we have \(6xy^{3}\sqrt{xy}\)

Answer:

\(6xy^{3}\sqrt{xy}\)