What is sqrt(n)*(sqrt(4n+1)+2sqrt(n)) ?

The solution to sqrt(n)*(sqrt(4n+1)+2sqrt(n)) is sqrt(n)sqrt(4n+1)+2n

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simplify sqrt(n)*(sqrt(4n+1)+2sqrt(n))

simplify

n \cdot (4 n + 1 + 2 n)

n 4 n + 1 + 2 n

Solution steps

n (4 n + 1 + 2 n)

Apply the distributive law:

a (b + c) = ab + a c

n (4 n + 1 + 2 n) = n 4 n + 1 + n \cdot 2 n

= n 4 n + 1 + n \cdot 2 n

Simplify

n \cdot 2 n : 2 n

= n 4 n + 1 + 2 n

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(1 + sin (x) - 1 - sin (x))^{2}

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What is sqrt(n)*(sqrt(4n+1)+2sqrt(n)) ?
The solution to sqrt(n)*(sqrt(4n+1)+2sqrt(n)) is sqrt(n)sqrt(4n+1)+2n