Solve (2-3)-1/2[5-(-3)^2]sqrt{(1/2)^2+(-4)^44}

$$( 2 - 3 ) - \frac { 1 } { 2 } [ 5 - ( - 3 ) ^ { 2 } ] \sqrt { ( \frac { 1 } { 2 } ) ^ { 2 } + ( - 4 ) ^ { 44 } }$$

Evaluate

$$5\sqrt{49517601571415210995964969}-1\approx 3.518437209 \cdot 10^{13}$$

Solution Steps

Subtract 3 from 2 to get -1.

$$-1-\frac{1}{2}\left(5-\left(-3\right)^{2}\right)\sqrt{\left(\frac{1}{2}\right)^{2}+\left(-4\right)^{44}}$$

Calculate -3 to the power of 2 and get 9.

$$-1-\frac{1}{2}\left(5-9\right)\sqrt{\left(\frac{1}{2}\right)^{2}+\left(-4\right)^{44}}$$

Subtract 9 from 5 to get -4.

$$-1-\frac{1}{2}\left(-4\right)\sqrt{\left(\frac{1}{2}\right)^{2}+\left(-4\right)^{44}}$$

Multiply \frac{1}{2} and -4 to get \frac{-4}{2}.

$$-1-\frac{-4}{2}\sqrt{\left(\frac{1}{2}\right)^{2}+\left(-4\right)^{44}}$$

Divide -4 by 2 to get -2.

$$-1-\left(-2\sqrt{\left(\frac{1}{2}\right)^{2}+\left(-4\right)^{44}}\right)$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$-1-\left(-2\sqrt{\frac{1}{4}+\left(-4\right)^{44}}\right)$$

Calculate -4 to the power of 44 and get 309485009821345068724781056.

$$-1-\left(-2\sqrt{\frac{1}{4}+309485009821345068724781056}\right)$$

Convert 309485009821345068724781056 to fraction \frac{1237940039285380274899124224}{4}.

$$-1-\left(-2\sqrt{\frac{1}{4}+\frac{1237940039285380274899124224}{4}}\right)$$

Since \frac{1}{4} and \frac{1237940039285380274899124224}{4} have the same denominator, add them by adding their numerators.

$$-1-\left(-2\sqrt{\frac{1+1237940039285380274899124224}{4}}\right)$$

Add 1 and 1237940039285380274899124224 to get 1237940039285380274899124225.

$$-1-\left(-2\sqrt{\frac{1237940039285380274899124225}{4}}\right)$$

Rewrite the square root of the division \sqrt{\frac{1237940039285380274899124225}{4}} as the division of square roots \frac{\sqrt{1237940039285380274899124225}}{\sqrt{4}}.

$$-1-\left(-2\times \frac{\sqrt{1237940039285380274899124225}}{\sqrt{4}}\right)$$

Factor 1237940039285380274899124225=5^{2}\times 49517601571415210995964969. Rewrite the square root of the product \sqrt{5^{2}\times 49517601571415210995964969} as the product of square roots \sqrt{5^{2}}\sqrt{49517601571415210995964969}. Take the square root of 5^{2}.

$$-1-\left(-2\times \frac{5\sqrt{49517601571415210995964969}}{\sqrt{4}}\right)$$

Calculate the square root of 4 and get 2.

$$-1-\left(-2\times \frac{5\sqrt{49517601571415210995964969}}{2}\right)$$

Cancel out 2 and 2.

$$-1-\left(-5\sqrt{49517601571415210995964969}\right)$$

The opposite of -5\sqrt{49517601571415210995964969} is 5\sqrt{49517601571415210995964969}.

$$-1+5\sqrt{49517601571415210995964969}$$

Factor

$$5 \sqrt{49517601571415210995964969} - 1 = 35184372088831$$