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Q.

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 10 2 .
⇒ 33.64 = 3364 100
Prime factorization of 3364=2×2×29×29.
⇒3364= 2 2 × 29 2
⇒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 = 58 2 10 2
⇒ 33.64 = 58 10
⇒ 33.64 =5.8
Thus, 33.64 =5.8.
 
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