To simplify the expression [tex]\(\sqrt{3} \times \sqrt{15}\)[/tex], we can use the property of square roots which states:
[tex]\[ \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} \][/tex]
Starting with our given expression:
[tex]\[ \sqrt{3} \times \sqrt{15} \][/tex]
We apply the property of square roots:
[tex]\[ \sqrt{3 \times 15} \][/tex]
Next, we perform the multiplication inside the square root:
[tex]\[ 3 \times 15 = 45 \][/tex]
So, our expression becomes:
[tex]\[ \sqrt{45} \][/tex]
Now, we evaluate the square root of 45. The numerical value of [tex]\(\sqrt{45}\)[/tex] is approximately [tex]\(6.708203932499369\)[/tex].
Thus, the simplified expression [tex]\(\sqrt{3} \times \sqrt{15}\)[/tex] equals [tex]\(\sqrt{45}\)[/tex], which numerically evaluates to approximately [tex]\(6.708203932499369\)[/tex].
