What is 3+sqrt((4m-2)^2-4) ?

The solution to 3+sqrt((4m-2)^2-4) is 3+4sqrt(m(m-1))

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simplify 3+sqrt((4m-2)^2-4)

simplify

3 + (4 m - 2)^{2} - 4

3 + 4 m (m - 1)

Solution steps

3 + (4 m - 2)^{2} - 4

Expand

(4 m - 2)^{2} - 4 : 16 m^{2} - 16 m

= 3 + 16 m^{2} - 16 m

Factor out common term

16 m : 16 m (m - 1)

= 3 + 16 m (m - 1)

Apply radical rule:

ab = a b,

assuming

a \geq 0, b \geq 0

16 m (m - 1) = 16 m (m - 1)

= 3 + 16 m (m - 1)

16 = 4

= 3 + 4 m (m - 1)

(2 x^{2} - 5) (x + 2)

35 + 20

a^{3} + 2 a^{2} - a - 2

∣ - 6 - 5 ∣

- \frac{1}{4} + \frac{3}{10}

What is 3+sqrt((4m-2)^2-4) ?
The solution to 3+sqrt((4m-2)^2-4) is 3+4sqrt(m(m-1))