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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

102 .

⇒ 156.25 = 15625100

Write the prime factorization of the fraction.

15625 = 5 × 5 × 5 × 5 × 5 × 5

⇒ 15625 = 52 × 52 × 52

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 = 1252102

⇒ 156.25 = 12510

⇒ 156.25 = 12.5

Thus,

156.25 = 12.5.

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