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Q.

The square root of 156.25 is ____.


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Detailed Solution

The square root of 156.25 is 12.5.
The given number is 156.25.
Convert the decimal value into a fraction by multiplying the numerator and the denominator with 10 2 .
  ⇒ 156.25 = 15625 100
Write the prime factorization of the fraction.
15625=5×5×5×5×5×5 ⇒15625= 5 2 × 5 2 × 5 2
As the powers are the same, bases can be multiplied.
⇒15625= (5×5×5) 2
⇒15625= (125) 2
Also, write 100=10×10.   ⇒100= (10) 2
Substitute the values from prime factorization in fraction, and we get,
⇒ 156.25 = 125 2 10 2
⇒ 156.25 = 125 10
⇒ 156.25 =12.5
Thus, 156.25 =12.5.
 
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