Question 390791: 16 plus 2 to the 5th power divided by 8 minus the square root of 36 plus 7
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! (6+2^(5))/(8-~(36+7))
Raising a number to the 5th power is the same as multiplying the number by itself 5 times. In this case, 2 raised to the 5th power is 32.
(6+32)/(8-~(36+7))
Add 32 to 6 to get 38.
(38)/(8-~(36+7))
Add 7 to 36 to get 43.
(38)/(8-~(43))
To rationalize the denominator of a fraction, rewrite the fraction so that the new fraction has the same value as the original and has a rational denominator. The factor to multiply by should be an expression that will eliminate the radical in the denominator. In this case, the expression that will eliminate the radical in the denominator is ((8+~(43)))/((8+~(43))).
(38)/(8-~(43))*(8+~(43))/(8+~(43))
Use the difference of squares formula to factor a^(2)-b^(2)=(a-b)(a+b).
(38(8+~(43)))/((8)^(2)-(-~(43))^(2))
Square each of the expressions in the factored denominator.
(38(8+~(43)))/(64-(43))
Simplify the rationalized expression.
(304+38~(43))/(64-(43))
Multiply -1 by the 43 inside the parentheses.
(304+38~(43))/(64-43)
Subtract 43 from 64 to get 21.
(304+38~(43))/(21)
Factor out the GCF of 38 from each term in the polynomial.
(38(8)+38(~(43)))/(21)
Factor out the GCF of 38 from 304+38~(43).
(38(8+~(43)))/(21)
The approximate value of ((6+2^(5)))/((8-~(36+7))) is 26.34203.
26.34203
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