n=5√10= ..........
Answers
Step-by-step explanation:
Step by Step Solution:
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Radical Equation entered :
√n+5-√n-10 = 1
Step by step solution :
STEP
1
:
Isolate a square root on the left hand side
Original equation
√n+5-√n-10 = 1
Isolate
√n+5 = √n-10+1
STEP
2
:
Eliminate the radical on the left hand side
Raise both sides to the second power
(√n+5)2 = (√n-10+1)2
After squaring
n+5 = n-10+1+2√n-10
STEP
3
:
Get remaining radical by itself
Current equation
n+5 = n-10+1+2√n-10
Isolate radical on the left hand side
-2√n-10 = -n-5+n-10+1
Tidy up
2√n-10 = 14
STEP
4
:
Eliminate the radical on the left hand side
Raise both sides to the second power
(2√n-10)2 = (14)2
After squaring
4n-40 = 196
STEP
5
:
Solve the linear equation
Rearranged equation
4n -236 = 0
Add 236 to both sides
4n = 236
Divide both sides by 4
A possible solution is :
n = 59
STEP
6
:
Check that the solution is correct
Original equation, root isolated, after tidy up
√n+5 = √n-10+1
Plug in 59 for n
√(59)+5 = √(59)-10+1
Simplify
√64 = 8
Solution checks !!
Solution is:
n = 59
One solution was found :
n = 59
One of the laws of indices deals with cases where there are powers and roots at the same time.
x
p
q
=
q
√
x
p
=
(
q
√
x
)
p
The denominator shows the root and the numerator gives the power.
Note that the power can be inside or outside the root.
I prefer to find the root first, and then raise to the power because this keeps the numbers smaller. They can usually be calculated mentally rather than needing a calculator
32
2
5
=
(
5
√
32
)
2
=
2
2
w
w
w
w
w
w
w
w
w
w
w
w
w
(
2
⋅
2
⋅
2
⋅
2
⋅
2
=
2
5
=
32
)
=
4
Compare this with the other method of squaring first.
5
√
32
2
=
5
√
1024
=
4
While I know that
2
5
=
32
, the square of
32
and the fifth root of
1024
are not facts that I would be able to recall from memory.