simpify √ √30 √21 / √30 √21
Answers
Answer:
x=√12+x. Then ... 1⇒ ⎷72 +√72+√72+√72+√72.... Solution→9. 2⇒ ⎷30+√30+√30+√30+√30.
Step-by-step explanation:
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Answer:
There is a really interesting math trick behind it.
If you see a question like this take out the number inside it (in this case is
12
)
Take consecutive numbers such as:
n
(
n
+
1
)
=
12
Always remember that the answer is
n
+
1
This is true because if you let the infinite nested radical function = x then realise that x is also also under the first root sign as:
x
=
√
12
+
x
Then, squaring both sides:
x
2
=
12
+
x
Or:
x
2
−
x
=
12
x
(
x
−
1
)
=
12
Now let
x
=
n
+
1
Then
n
(
n
+
1
)
=
12
With the answer to the infinite nested radical function (x) being equal to
n
+
1
If you solve it you get
n
=
3
and
n
+
1
=
4
So,
The answer is
4
Practice problems:
1
⇒
⎷
72
+
√
72
+
√
72
+
√
72
+
√
72
...
.
S
o
l
u
t
i
o
n
→
9
2
⇒
⎷
30
+
√
30
+
√
30
+
√
30
+
√
30
...
.
S
o
l
u
t
i
o
n
→
6
And wait!!!
If you see a question like
⎷
72
−
√
72
−
√
72
−
√
72
−
√
72
...
.
n
is the solution (in this case is
8
)
Problems to solve on your own
⎷
1056
+
√
1056
+
√
1056
+
√
1056
+
√
1056
...
.
⎷
110
+
√
110
+
√
110
+
√
110
+
√
110
...
.