What is (3n^2+sqrt(2n^2))/(sqrt(10n)) ?

The solution to (3n^2+sqrt(2n^2))/(sqrt(10n)) is (sqrt(n)(3n+sqrt(2)))/(sqrt(10))

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simplify (3n^2+sqrt(2n^2))/(sqrt(10n))

simplify

\frac{3 n ^{2} + 2 n ^{2}}{10 n}

\frac{n ( 3 n + 2 )}{10}

Solution steps

\frac{3 n ^{2} + 2 n ^{2}}{10 n}

Simplify

2 n^{2} : 2 n

= \frac{3 n ^{2} + 2 n}{10 n}

Factor

3 n^{2} + 2 n : n (3 n + 2)

= \frac{n ( 3 n + 2 )}{10 n}

Apply radical rule:

ab = a b,

assuming

a \geq 0, b \geq 0

10 n = n 10

= \frac{n ( 3 n + 2 )}{n 10}

Apply radical rule:

a = a a

n = n n

= \frac{n n ( 3 n + 2 )}{n 10}

Cancel the common factor:

n

= \frac{n ( 3 n + 2 )}{10}

(x - 14)^{2} = 2

\frac{7}{4} \cdot 6

2 b^{2} + 3 b = 1

4 m = 25

3 x - 17 = 4

What is (3n^2+sqrt(2n^2))/(sqrt(10n)) ?
The solution to (3n^2+sqrt(2n^2))/(sqrt(10n)) is (sqrt(n)(3n+sqrt(2)))/(sqrt(10))