Question

now use the equation to solve for the value of c. start by rewriting each exponent as a single number to make this equation easier to work with. find the value of 7² first.
a = 7
c =?
b = 4
$a^{2}+b^{2}=c^{2}$
$7^{2}+4^{2}=c^{2}$
$\square + 4^{2}=c^{2}$

Explanation:

Step1: Calculate $7^2$

$7^2=7\times7 = 49$

Step2: Substitute into the Pythagorean theorem

Substitute $7^2 = 49$ into $7^2+4^2=c^2$, we get $49 + 4^2=c^2$. Then calculate $4^2=4\times4 = 16$. So the equation becomes $49+16=c^2$, and $c^2=65$.

Step3: Solve for $c$

$c=\sqrt{65}$

Answer:

$c = \sqrt{65}$