Question

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

Answer 1

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

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=√(c^2-a^2)`

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

`b=√(c^2-a^2) \\b=√((4)^2-(3)^2)\\ b=√((4*4)-(3*3))\\ b=√(16-9)\\b=√(7)`

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