What is (sqrt(1+\sqrt{p)}-2)(sqrt(1+\sqrt{p)}+2) ?

The solution to (sqrt(1+\sqrt{p)}-2)(sqrt(1+\sqrt{p)}+2) is sqrt(p)-3

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simplify (sqrt(1+\sqrt{p)}-2)(sqrt(1+\sqrt{p)}+2)

simplify

(1 + p - 2) (1 + p + 2)

p - 3

Solution steps

(1 + p - 2) (1 + p + 2)

Apply Difference of Two Squares

(1 + p - 2) (1 + p + 2) : p - 3

= p - 3

(y = 2, x + 6) (\frac{x}{2} - y = 3)

- 3 (7 - 14)

- \frac{3 ( 199 + 77 73 )}{8} + 1715 + 25073

(\frac{v}{2} - 1) \cdot (y + vu)

2 (35 - 5)

What is (sqrt(1+\sqrt{p)}-2)(sqrt(1+\sqrt{p)}+2) ?
The solution to (sqrt(1+\sqrt{p)}-2)(sqrt(1+\sqrt{p)}+2) is sqrt(p)-3