Question

the square root function
quiz complete
1 2 3
what is the simplified form of \\(\sqrt{64x^{16}}\\)?
\\(8x^4\\)
\\(8x^8\\)
\\(32x^4\\)
\\(32x^8\\)

Explanation:

Step1: Simplify the square root of 64

The square root of 64 is 8, since \(8\times8 = 64\). So, \(\sqrt{64}=8\).

Step2: Simplify the square root of \(x^{16}\)

Using the property of exponents \(\sqrt{a^m}=a^{\frac{m}{2}}\), for \(a = x\) and \(m = 16\), we have \(\sqrt{x^{16}}=x^{\frac{16}{2}}=x^{8}\).

Step3: Combine the results

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\)), we get \(\sqrt{64x^{16}}=\sqrt{64}\times\sqrt{x^{16}} = 8\times x^{8}=8x^{8}\).

Answer:

B. \(8x^{8}\)