Solve x^2=7^8
by inspection. There are two real solutions. Enter the lesser number first, and use exponents in your responses
Taking the square root of both sides, we have:
x = ±√(7^8)
Since we are looking for the lesser solution, we take the negative square root:
x = -√(7^8)
x = -7^4
So, the solution is x = -2401
To solve the equation x^2 = 7^8 by inspection, we need to find the square root of 7^8.
Taking the square root of both sides of the equation, we have:
x = ± √(7^8)
To simplify the expression inside the square root, we can rewrite it as (7^4)^2:
x = ± √((7^4)^2)
Using the property of exponents that states (a^b)^c = a^(b*c):
x = ± (7^4)
Now, let's calculate 7^4:
7^4 = 7 * 7 * 7 * 7 = 2401
So, the square root of 7^8 is equal to the square root of (7^4)^2, which simplifies to:
x = ± 2401
Therefore, the two real solutions to the equation x^2 = 7^8 are:
x = -2401 and x = 2401
The lesser number is -2401, so the final answer is:
-2401, 2401
To solve the equation x^2 = 7^8 by inspection, we need to find the square root of both sides. Remember, the square root of a number is the value that, when multiplied by itself, gives the original number.
Now, let's find the square root of both sides:
√(x^2) = √(7^8)
Since we're looking for two real solutions (positive and negative), we can use both the positive and negative square roots:
x = ± √(7^8)
To simplify further, let's convert 7^8 into a single number.
7^8 = (7^4)^2
Next, calculate:
7^4 = 2401
Thus:
7^8 = (2401)^2
Now we can substitute this back into the equation:
x = ± √((2401)^2)
Taking the square root of (2401)^2:
x = ± 2401
So, the two real solutions for x are -2401 and 2401. Enter the lesser number first:
x = -2401, 2401