Question

Solve for B. Enter the number that goes under the radical Symbol​

Answer 1

Answer:

The number that goes beneath the radical is $7$.

Step-by-step explanation:

If you are dealing with any right triangle with $2$ given sides, using the Pythagorean Theorem, as shown below, makes things relatively simple.

- Pythagorean Theorem: $a^2+b^2=c^2$

• $a$ and $b$ are both the smaller sides of the triangle, while $c$ is the hypotenuse (the longest side of the triangle).

In this case, we have 4 equivalent right triangles with given sides $3$ and $4$ for the hypotenuse, so let's see what we need to solve for by writing down what we know in a form following the Pythagorean Theorem.

Equation:

$a^2+b^2=c^2$

Given:

$a=3$

$b=$ ?

$c=4$

Work:

$a^2+b^2=c^2$

• Isolate the unknown value without plugging in our known values yet. This step is unnecessary, but can help if you have trouble with making mistakes with your algebra.

$a^2+b^2=c^2\\b^2=c^2-a^2\\b=\sqrt{c^2-a^2}$

• Plug in our given values and solve for $b$.

$b=\sqrt{c^2-a^2} \\b=\sqrt{(4)^2-(3)^2}\\ b=\sqrt{(4*4)-(3*3)}\\ b=\sqrt{16-9}\\b=\sqrt{7}$

The number that goes beneath the radical is $7$.