Mixing
Simplifying a solution to $x^2 = 4 + 2sqrt{2}$
1
$begingroup$
$$x^2 = 4 + 2sqrt{2}$$
$$x = 2 + sqrt{2sqrt{2}}$$
Neglecting that the result can be negative as well, how should I continue? How can I simplify it?
algebra-precalculus radicals
edited Jan 23 at 21:10
J. W. Tanner
3,2401320
asked Jan 23 at 18:37
wenoweno
29911
$endgroup$
add a comment |
1
$begingroup$
$$x^2 = 4 + 2sqrt{2}$$
$$x = 2 + sqrt{2sqrt{2}}$$
Neglecting that the result can be negative as well, how should I continue? How can I simplify it?
algebra-precalculus radicals
edited Jan 23 at 21:10
J. W. Tanner
3,2401320
asked Jan 23 at 18:37
wenoweno
29911
$endgroup$
6
$begingroup$
Note that $sqrt {a+b}neq sqrt a +sqrt b$ in general
$endgroup$
– Mark Bennet
Jan 23 at 18:39
3
$begingroup$
Why simplify the expression if it's already simple? :o)
$endgroup$
– Bernard
Jan 23 at 18:43
add a comment |
1
1
1
$begingroup$
$$x^2 = 4 + 2sqrt{2}$$
$$x = 2 + sqrt{2sqrt{2}}$$
Neglecting that the result can be negative as well, how should I continue? How can I simplify it?
algebra-precalculus radicals
edited Jan 23 at 21:10
J. W. Tanner
3,2401320
asked Jan 23 at 18:37
wenoweno
29911
$endgroup$
$$x^2 = 4 + 2sqrt{2}$$
$$x = 2 + sqrt{2sqrt{2}}$$
Neglecting that the result can be negative as well, how should I continue? How can I simplify it?
algebra-precalculus radicals
algebra-precalculus radicals
edited Jan 23 at 21:10
J. W. Tanner
3,2401320
asked Jan 23 at 18:37
wenoweno
29911
edited Jan 23 at 21:10
J. W. Tanner
3,2401320
asked Jan 23 at 18:37
wenoweno
29911
edited Jan 23 at 21:10
J. W. Tanner
3,2401320
edited Jan 23 at 21:10
J. W. Tanner
3,2401320
edited Jan 23 at 21:10
J. W. Tanner
3,2401320
3,2401320
asked Jan 23 at 18:37
wenoweno
29911
asked Jan 23 at 18:37
wenoweno
29911
asked Jan 23 at 18:37
wenoweno
29911
29911
6
$begingroup$
Note that $sqrt {a+b}neq sqrt a +sqrt b$ in general
$endgroup$
– Mark Bennet
Jan 23 at 18:39
3
$begingroup$
Why simplify the expression if it's already simple? :o)
$endgroup$
– Bernard
Jan 23 at 18:43
add a comment |
6
$begingroup$
Note that $sqrt {a+b}neq sqrt a +sqrt b$ in general
$endgroup$
– Mark Bennet
Jan 23 at 18:39
3
$begingroup$
Why simplify the expression if it's already simple? :o)
$endgroup$
– Bernard
Jan 23 at 18:43
6
6
$begingroup$
Note that $sqrt {a+b}neq sqrt a +sqrt b$ in general
$endgroup$
– Mark Bennet
Jan 23 at 18:39
$begingroup$
Note that $sqrt {a+b}neq sqrt a +sqrt b$ in general
$endgroup$
– Mark Bennet
Jan 23 at 18:39
3
3
$begingroup$
Why simplify the expression if it's already simple? :o)
$endgroup$
– Bernard
Jan 23 at 18:43
$begingroup$
Why simplify the expression if it's already simple? :o)
$endgroup$
– Bernard
Jan 23 at 18:43
add a comment |
1 Answer
1
active
oldest
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5
$begingroup$
$x^2 = 4 + 2sqrt{2} rightarrow x = pm sqrt{4 + 2sqrt{2}}$
answered Jan 23 at 18:40
lightxbulblightxbulb
1,125311
$endgroup$
add a comment |
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5
$begingroup$
$x^2 = 4 + 2sqrt{2} rightarrow x = pm sqrt{4 + 2sqrt{2}}$
answered Jan 23 at 18:40
lightxbulblightxbulb
1,125311
$endgroup$
add a comment |
5
$begingroup$
$x^2 = 4 + 2sqrt{2} rightarrow x = pm sqrt{4 + 2sqrt{2}}$
answered Jan 23 at 18:40
lightxbulblightxbulb
1,125311
$endgroup$
add a comment |
5
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5
$begingroup$
$x^2 = 4 + 2sqrt{2} rightarrow x = pm sqrt{4 + 2sqrt{2}}$
answered Jan 23 at 18:40
lightxbulblightxbulb
1,125311
$endgroup$
$x^2 = 4 + 2sqrt{2} rightarrow x = pm sqrt{4 + 2sqrt{2}}$
answered Jan 23 at 18:40
lightxbulblightxbulb
1,125311
answered Jan 23 at 18:40
lightxbulblightxbulb
1,125311
answered Jan 23 at 18:40
lightxbulblightxbulb
1,125311
answered Jan 23 at 18:40
lightxbulblightxbulb
1,125311
1,125311
add a comment |
add a comment |
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6
$begingroup$
Note that $sqrt {a+b}neq sqrt a +sqrt b$ in general
$endgroup$
– Mark Bennet
Jan 23 at 18:39
3
$begingroup$
Why simplify the expression if it's already simple? :o)
$endgroup$
– Bernard
Jan 23 at 18:43