3 Ways To Calculate Square Root Of 175

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Calculating the square root of a number can be a simple yet fascinating mathematical operation. In this article, we will explore three different methods to calculate the square root of 175.

Method 1: Using a Calculator

One of the easiest ways to calculate the square root of 175 is by using a calculator. Simply enter the number 175 and press the square root button (√). The calculator will instantly display the result, which is approximately 13.23.

Method 2: Factoring Method

The factoring method involves breaking down the number into its prime factors and then finding the square root of each factor. To calculate the square root of 175 using this method, we need to factorize 175:

175 = 5 × 5 × 7

Now, we can find the square root of each factor:

√175 = √(5 × 5 × 7) = √5 × √5 × √7 = 5√7 ≈ 13.23

Method 3: Long Division Method

The long division method is a more complex and time-consuming method, but it can be useful for larger numbers. To calculate the square root of 175 using this method, we need to divide 175 by a series of perfect squares:

175 ÷ 1 = 175 175 ÷ 4 = 43.75 175 ÷ 9 = 19.44 175 ÷ 16 = 10.94 175 ÷ 25 = 7

Now, we can find the average of the last two results:

(10.94 + 7) / 2 = 8.97

Repeat the process until the average value converges to a single value, which is approximately 13.23.

Gallery of Square Root Calculations

In conclusion, calculating the square root of 175 can be done using various methods, including using a calculator, factoring, and long division. Each method has its own advantages and disadvantages, and the choice of method depends on the individual's preference and the complexity of the calculation.

We hope this article has been informative and helpful in your mathematical endeavors. If you have any questions or would like to share your own methods for calculating square roots, please leave a comment below.

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