To determine the simplest form of [tex]\(\sqrt{343}\)[/tex], we start by finding the prime factorization of the number 343.
343 can be written as follows:
[tex]\[ 343 = 7 \times 49 \][/tex]
[tex]\[ 343 = 7 \times 7 \times 7 \][/tex]
[tex]\[ 343 = 7^3 \][/tex]
Next, we need to compute the square root of 343:
[tex]\[ \sqrt{343} = \sqrt{7^3} \][/tex]
[tex]\[ \sqrt{343} = \sqrt{7^2 \times 7} \][/tex]
[tex]\[ \sqrt{343} = \sqrt{(7^2) \times 7} \][/tex]
[tex]\[ \sqrt{343} = \sqrt{7^2} \times \sqrt{7} \][/tex]
[tex]\[ \sqrt{343} = 7 \times \sqrt{7} \][/tex]
Thus, the simplest form of [tex]\(\sqrt{343}\)[/tex] is:
[tex]\[ 7 \sqrt{7} \][/tex]
Therefore, the correct answer is:
[tex]\[ 7 \sqrt{7} \][/tex]
