The process of taking the square root of a number and then raising it to the fourth power may seem complex at first, but it can be simplified using basic mathematical principles.
To start, let’s break it down into two parts: finding the square root and then raising that result to the power of four.
1. **Square Root**: The square root of a number ‘x’, denoted as √x, is a value that, when multiplied by itself, gives ‘x’. For example, the square root of 16 is 4, because 4 × 4 = 16.
2. **Raising to the Fourth Power**: Once you have the square root (let’s call it ‘y’), raising it to the fourth power means computing y²². In simpler terms, if you have the square root of ‘x’ (√x), and you raise it to the fourth power, you can express this mathematically as (√x)⁴.
Now, using the property of exponents, you can combine these operations:
(√x)⁴ = (x^(1/2))⁴ = x^(1/2 * 4) = x².
Thus, the square root of a number raised to the fourth power essentially equals the original number squared.
For example:
Let’s calculate it for x = 16:
(√16)⁴ = (4)⁴ = 256.
This demonstrates that taking the square root of 16 and then raising it to the fourth power yields the result of 256, which is indeed equal to 16².
So in summary, taking the square root of a number and then raising it to the fourth power effectively gives you the square of that number. It’s a beautiful interplay of mathematics that highlights how different operations can be related!