To express [tex]\(\sqrt{6} \times \sqrt{8}\)[/tex] in the form [tex]\(a \sqrt{3}\)[/tex], we can follow these steps:
1. Use the property of square roots: We know that [tex]\(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}\)[/tex]. Thus,
[tex]\[
\sqrt{6} \times \sqrt{8} = \sqrt{6 \times 8}
\][/tex]
2. Multiply the numbers under the square root:
[tex]\[
6 \times 8 = 48
\][/tex]
So,
[tex]\[
\sqrt{6} \times \sqrt{8} = \sqrt{48}
\][/tex]
3. Simplify the square root: We recognize that 48 can be factored into 16 and 3, where 16 is a perfect square.
[tex]\[
48 = 16 \times 3
\][/tex]
This allows us to rewrite the square root as:
[tex]\[
\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3}
\][/tex]
4. Take the square root of the perfect square:
[tex]\[
\sqrt{16} = 4
\][/tex]
Therefore,
[tex]\[
\sqrt{48} = 4 \sqrt{3}
\][/tex]
Thus, [tex]\( \sqrt{6} \times \sqrt{8} \)[/tex] written in the form [tex]\( a \sqrt{3} \)[/tex] is:
[tex]\[
4 \sqrt{3}
\][/tex]
So, [tex]\( a = 4 \)[/tex].
