Rationalize the denominator and simplify: 12 / √7 + 2

1 answer:

4 0

Multiply
12
√
7
+
2
12
7
+
2
by
√
7
−
2
√
7
−
2
7
-
2
7
-
2
.
12
√
7
+
2
⋅
√
7
−
2
√
7
−
2
12
7
+
2
⋅
7
-
2
7
-
2
Multiply
12
√
7
+
2
12
7
+
2
and
√
7
−
2
√
7
−
2
7
-
2
7
-
2
.
12
(
√
7
−
2
)
(
√
7
+
2
)
(
√
7
−
2
)
12
(
7
-
2
)
(
7
+
2
)
(
7
-
2
)
Expand the denominator using the FOIL method.
12
(
√
7
−
2
)
√
7
2
+
√
7
⋅
−
2
+
2
√
7
−
4
12
(
7
-
2
)
7
2
+
7
⋅
-
2
+
2
7
-
4
Simplify.
12
(
√
7
−
2
)
3
12
(
7
-
2
)
3
Cancel the common factor of
12
12
and
3
3
.
Tap for more steps...
4
(
√
7
−
2
)
4
(
7
-
2
)
Apply the distributive property.
4
√
7
+
4
⋅
−
2
4
7
+
4
⋅
-
2
Multiply
4
4
by
−
2
-
2
.
4
√
7
−
8
4
7
-
8
The result can be shown in multiple forms.
Exact Form:
4
√
7
−
8
4
7
-
8
Decimal Form:
2.58300524
…

You might be interested in

Match the information on the left with the appropriate equation on the right.

zaharov [31]

Answer:

See attachment below

Step-by-step explanation:

For the first option, we are given m = - 2 / 3, b = 3. This is likely in the point - slope form y = mx + b, where m = slope and b = y - intercept. Thus, the equation of the line in point - slope form given this information, should be y = - 2 / 3x + 3. It seems as if none of the following equations match this form, so let us interchange the equation a bit,

y = - 2 / 3x + 3,

y + 2 / 3x = 3,

2x + 3y = 9 - Option C

_______________________________________________________

Next we are given m = - 3 / 2, and that this line passes through the point ( 4, - 1 ). Substitute m as - 3 / 2, x as 4, y as - 1, knowing point ( 4, - 1 ), into the form y = mx + b - solving for b.

- 1 = ( - 3 / 2 )( 4 ) + b,

b = 5,

Thus the equation in point - slope form should be y = - 3 / 2x + 5. None of the choices match this, so let us again alter the equation,

y = - 3 / 2x + 5,

2y = - 3x + 10,

- 2y = 3x - 10 - Option A

_______________________________________________________

( 6, 3 ) and ( 3, 1 ) is given to lie on this line. The slope of the line should be as follows,

Slope = 3 - 1 / 6 - 3 = 2 / 3

Now let us determine the y - intercept ( b ) by substitute one of the points, say ( 6, 3 ). In this case x = 6, and y = 3,

3 = ( 2 / 3 )( 6 ) + b,

b = - 1,