Question

the square root function
quiz complete
1 2
what is the simplified form of \\(\sqrt{100x^{36}}\\) ?
\\(\circ\\) \\(10x^{18}\\)
\\(\circ\\) \\(10x^{6}\\)
\\(\circ\\) \\(50x^{18}\\)
\\(\circ\\) \\(50x^{6}\\)

Explanation:

Step1: Simplify the square root of 100

The square root of 100 is 10, since \(10\times10 = 100\). So, \(\sqrt{100}=10\).

Step2: Simplify the square root of \(x^{36}\)

Using the property of exponents \(\sqrt{a^m}=a^{\frac{m}{2}}\) (for \(a\geq0\) and \(m\) even), for \(a = x\) and \(m = 36\), we have \(\sqrt{x^{36}}=x^{\frac{36}{2}}=x^{18}\).

Step3: Combine the results

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0\) and \(b\geq0\)), we have \(\sqrt{100x^{36}}=\sqrt{100}\times\sqrt{x^{36}} = 10\times x^{18}=10x^{18}\).

Answer:

\(10x^{18}\) (corresponding to the option "10\(x^{18}\)")