Question

what is the squaroot of 192 I simplest form

Answer 1

To express \(\sqrt{192}\) in its simplest form, we can first factor 192 into its prime factors.

1. Start with the prime factorization of 192:
\[
192 \div 2 = 96 \\
96 \div 2 = 48 \\
48 \div 2 = 24 \\
24 \div 2 = 12 \\
12 \div 2 = 6 \\
6 \div 2 = 3 \\
3 \div 3 = 1
\]
Thus, the prime factorization of 192 is:
\[
192 = 2^6 \times 3^1
\]

2. Now, apply the square root:
\[
\sqrt{192} = \sqrt{2^6 \times 3^1}
\]

3. Use the property of square roots:
\[
\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}
\]
Therefore:
\[
\sqrt{192} = \sqrt{2^6} \times \sqrt{3^1} = 2^{6/2} \times 3^{1/2} = 2^3 \times \sqrt{3} = 8\sqrt{3}
\]

So, the simplest form of \(\sqrt{192}\) is:
\[
\sqrt{192} = 8\sqrt{3}
\]