Algebra: Solving for X using Difference of Squares (√(100² - 96²))

Published on April 12, 2025

Algebra

Solve for X in the equation X = √(100² - 96²). This problem involves simplifying the expression using the difference of squares formula and calculating the square root.

Question

Answer

The problem is to calculate the value of

given by the equation:

We can solve this problem step by step:

Step 1: Recognize the expression inside the square root as a difference of squares.
The expression inside the square root is in the form

, where

and

.
We know that the difference of squares can be factored as

Step 2: Apply the difference of squares formula.
Using the formula, we can rewrite the expression inside the square root as:

Step 3: Calculate the values of

and

Step 4: Substitute these values back into the expression.

Step 5: Substitute this back into the original equation for

Step 6: Use the property of square roots

Step 7: Calculate the square roots of 4 and 196.
We know that

.
To find

, we can think of numbers whose square is close to 196. We know

and

. So the square root of 196 is between 10 and 20. Let’s try

.
So,

Step 8: Multiply the square roots.

Final Answer: The final answer is

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