Final answer:
To solve the equation x² = 5, we find that x is either the positive or negative square root of 5, which can also be expressed using a fractional exponent as x = ±5¹/2.
Step-by-step explanation:
To solve the equation x² = 5 using exponents, we need to find the value for x which, when squared, gives us 5. This means we are looking for a square root because we are essentially reversing the squaring process. Let's express 5 as a square in fractional exponent form.
Given that the square of 5 (√5) multiplied by itself equals 5 (5 · 5 = 5²), we can use this understanding to write 5 as 5¹/2. Hence, 5¹/2 is another way to write the square root of 5.
Using this knowledge, we can rewrite the original equation as:
x² = 5¹/2
To find x, we take the square root of both sides of the equation, which yields:
x = ±5¹/2
This means that x can be either the positive or negative square root of 5. In fractional exponent form, we express this as x = ±5¹/2.