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What is [tex]$\sqrt{343}$[/tex] in simplest form?

A. [tex]$49 \sqrt{7}$[/tex]

B. [tex][tex]$7 \sqrt{7}$[/tex][/tex]

C. [tex]$7 \sqrt{49}$[/tex]

D. 7


Sagot :

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]