Find the square root of the following: 156.25.

To find the square root of 156.25, we can approach it step by step. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we want to determine what number multiplied by itself equals 156.25.

Breaking Down the Problem

First, let's consider the number 156.25. It can be helpful to express it as a fraction or to recognize it as a decimal. Notably, 156.25 can also be written as:

• 156.25 = 15625/100

This representation shows that we are dealing with a perfect square since both the numerator and the denominator can be simplified further.

Finding the Square Root

Now, let's find the square root of both the numerator and the denominator separately:

• The square root of 15625 is 125 (since 125 x 125 = 15625).
• The square root of 100 is 10 (since 10 x 10 = 100).

Now, we can combine these results to find the square root of the entire fraction:

√(156.25) = √(15625/100) = √15625 / √100 = 125 / 10 = 12.5.

Verification

To ensure our answer is correct, we can square 12.5 and check if we return to the original number:

• 12.5 x 12.5 = 156.25.

This confirms that our calculation is accurate. Therefore, the square root of 156.25 is indeed 12.5.

Conclusion

In summary, the square root of 156.25 is 12.5. This method of breaking down the problem into manageable parts, along with verification, helps reinforce our understanding of square roots and their calculations.