Question

what is the square root of $16x^{36}$?
$\bigcirc\\ 4x^6$
$\bigcirc\\ 4x^{18}$
$\bigcirc\\ 8x^6$
$\bigcirc\\ 8x^{18}$

Explanation:

Step1: Recall square root properties

The square root of a product is the product of the square roots, i.e., $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ for non - negative $a,b$. Also, $\sqrt{a^{m}}=a^{\frac{m}{2}}$ when $a\geq0$.

Step2: Find square root of 16

We know that $\sqrt{16} = 4$ because $4\times4 = 16$.

Step3: Find square root of $x^{36}$

Using the property $\sqrt{a^{m}}=a^{\frac{m}{2}}$, for $a = x$ and $m = 36$, we have $\sqrt{x^{36}}=x^{\frac{36}{2}}=x^{18}$.

Step4: Combine the results

Using the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$, we get $\sqrt{16x^{36}}=\sqrt{16}\cdot\sqrt{x^{36}} = 4x^{18}$.

Answer:

B. $4x^{18}$ (assuming the second option is labeled as B, with the option text $4x^{18}$)