What is expand sqrt(1+(x^2(9x^2+6))) ?

The solution to expand sqrt(1+(x^2(9x^2+6))) is 3x^2+1

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expand sqrt(1+(x^2(9x^2+6)))

expand

1 + (x^{2} (9 x^{2} + 6))

3 x^{2} + 1

Solution steps

1 + (x^{2} (9 x^{2} + 6))

Remove parentheses:

(a) = a

= 1 + x^{2} (9 x^{2} + 6)

Expand

1 + x^{2} (9 x^{2} + 6) : 1 + 9 x^{4} + 6 x^{2}

= 1 + 9 x^{4} + 6 x^{2}

Factor

9 x^{4} + 6 x^{2} + 1 : (3 x^{2} + 1)^{2}

= (3 x^{2} + 1)^{2}

Apply radical rule:

assuming

a \geq 0

= 3 x^{2} + 1

\frac{f ( x + h )}{h}

\frac{1}{s ^{2} ( s + 0.5 )}

\frac{x ( x - 8 )}{2 ( x + 7 )}

\frac{x}{( x + 1 ) ( x - 1 ) ^{3}}

\frac{4 a}{2 a}

What is expand sqrt(1+(x^2(9x^2+6))) ?
The solution to expand sqrt(1+(x^2(9x^2+6))) is 3x^2+1