Solve 27-[38-\ 46-(15- overline 13-12) \ ]

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Question

$$27-[38-\{46-(15-\overline{13-12)}\}]$$

Evaluate

$2\left(\sqrt{3}+10\right)\approx 23.464101615$

Solution Steps

Factor $12=2^{2}\times 3$. Rewrite the square root of the product $\sqrt{2^{2}\times 3}$ as the product of square roots $\sqrt{2^{2}}\sqrt{3}$. Take the square root of $2^{2}$.

$$27-\left(38-\left(46-\left(15-2\sqrt{3}\right)\right)\right)$$

To find the opposite of $15-2\sqrt{3}$, find the opposite of each term.

$$27-\left(38-\left(46-15-\left(-2\sqrt{3}\right)\right)\right)$$

Subtract $15$ from $46$ to get $31$.

$$27-\left(38-\left(31-\left(-2\sqrt{3}\right)\right)\right)$$

The opposite of $-2\sqrt{3}$ is $2\sqrt{3}$.

$$27-\left(38-\left(31+2\sqrt{3}\right)\right)$$

To find the opposite of $31+2\sqrt{3}$, find the opposite of each term.

$$27-\left(38-31-2\sqrt{3}\right)$$

Subtract $31$ from $38$ to get $7$.

$$27-\left(7-2\sqrt{3}\right)$$

To find the opposite of $7-2\sqrt{3}$, find the opposite of each term.

$$27-7-\left(-2\sqrt{3}\right)$$

Subtract $7$ from $27$ to get $20$.

$$20-\left(-2\sqrt{3}\right)$$