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Find the value of $\sqrt{2401}$ using the prime factorization method.

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answer is D.

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Detailed Solution

Concept- firstly find the LCM and then solve the numbers with multiplication of factors then arrange them in pairs and take the square root of both sides. By using the prime factorization method.
Find the LCM of given number 2401,
Question Image

2401 = 7

\times

\times

\times

7
2401 =

7^{2} \times 7^{2}

2401 =

({7 \times 7)}^{2}

2401 =

{(49)}^{2}

Take the square root on both the sides,

\sqrt{2401}

\sqrt{{(49)}^{2}}

\sqrt{2401}

=49
Hence, the correct option is 4

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