find the simplified product: $sqrt{2x^{3}}cdotsqrt{18x^{5}}$ $sqrt{6x^{4}}$ $sqrt{36x^{8}}$ $18x^{4}$…
find the simplified product: $sqrt{2x^{3}}cdotsqrt{18x^{5}}$ $sqrt{6x^{4}}$ $sqrt{36x^{8}}$ $18x^{4}$ $6x^{4}$ done
Answer
Explanation:
Step1: Multiply the numbers under the square - roots
$\sqrt{2x^{3}}\cdot\sqrt{18x^{5}}=\sqrt{2x^{3}\cdot18x^{5}}$
Step2: Multiply the coefficients and add the exponents of $x$
$2\times18 = 36$ and $x^{3}\cdot x^{5}=x^{3 + 5}=x^{8}$, so $\sqrt{2x^{3}\cdot18x^{5}}=\sqrt{36x^{8}}$
Step3: Simplify the square - root
$\sqrt{36x^{8}}=\sqrt{36}\cdot\sqrt{x^{8}}$. Since $\sqrt{36}=6$ and $\sqrt{x^{8}}=x^{4}$, we get $6x^{4}$
Answer:
$6x^{4}$