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The square root of $33.64$ is ____.

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Detailed Solution

The square root of 33.64 is 5.8.
The given number is 33.64.
Convert the decimal value into a fraction by multiplying the numerator and the denominator with

102 .

⇒ 33.64 = 3364100

Prime factorization of

3364 = 2 × 2 × 29 × 29.

⇒ 3364 = 22 × 292

⇒ 3364 = (2 × 29) 2

⇒ 3364 = (58) 2

Also, write

100 = 10 × 10.

⇒ 100 = (10) 2

Now, substituting the values from prime factorization in fraction we get,

⇒ 33.64 = 582102

⇒ 33.64 = 5810

⇒ 33.64 = 5.8

Thus,

33.64 = 5.8.

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