What is sqrt(81+18\sqrt{7)+7} ?

The solution to sqrt(81+18\sqrt{7)+7} is sqrt(7)+9

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simplify sqrt(81+18\sqrt{7)+7}

simplify

81 + 187 + 7

7 + 9

Decimal

11.64575 \dots

Solution steps

81 + 187 + 7

Add the numbers:

81 + 7 = 88

= 88 + 187

= 7 + 187 + 81

= (7)^{2} + 187 + (81)^{2}

81 = 9

= (7)^{2} + 187 + 9^{2}

27 \cdot 9 = 187

= (7)^{2} + 27 \cdot 9 + 9^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(7)^{2} + 27 \cdot 9 + 9^{2} = (7 + 9)^{2}

= (7 + 9)^{2}

Apply radical rule:

n a^{n} = a

(7 + 9)^{2} = 7 + 9

= 7 + 9

\frac{2}{3} + \frac{1}{4} \cdot \frac{2}{5} - \frac{3}{4} + \frac{5}{2}

- 6 + i^{335} + 8 i^{87} + - 121

tan (x) + cot (x)

\frac{sin ( x )}{cos ^{2} ( x )}

1 - tan^{2} (x)

What is sqrt(81+18\sqrt{7)+7} ?
The solution to sqrt(81+18\sqrt{7)+7} is sqrt(7)+9