Question

which is a simpler form of the radical expression?
\sqrt3{27x^{15}y^{24}}
options:
a) 3x^{12}y^{21}
b) 3x^{5}y^{8}
c) 9x^{5}y^{8}
d) 9x^{15}y^{24}

Explanation:

Step1: Simplify the cube root of 27

The cube root of 27 is 3, since \(3^3 = 27\). So, \(\sqrt[3]{27}=3\).

Step2: Simplify the cube root of \(x^{15}\)

Using the property of radicals \(\sqrt[n]{a^m}=a^{\frac{m}{n}}\), for \(n = 3\) and \(m = 15\), we have \(x^{\frac{15}{3}}=x^5\).

Step3: Simplify the cube root of \(y^{24}\)

Using the same radical property, for \(n = 3\) and \(m = 24\), we get \(y^{\frac{24}{3}}=y^8\).

Step4: Combine the simplified parts

Multiply the simplified parts together: \(3\times x^5\times y^8 = 3x^5y^8\).

Answer:

B. \(3x^5y^8\)