Simplify three ninths times the quantity 1 plus the square root of 25 end quantity squared minus the quantity five minus one end quantity cubed.
a) −62
b) −52
c) 8
d) 52
First, let's simplify each part of the expression step by step:
1 + √25 = 1 + 5 = 6
5 - 1 = 4
Now, let's substitute these values back into the expression:
3/9 * (1 + √25)^2 - (5 - 1)^3
= 3/9 * 6^2 - 4^3
= 3/9 * 36 - 64
= 1/3 * 36 - 64
= 12 - 64
= -52
Therefore, the simplified expression is -52.
The answer is b) -52.
We will simplify the expression step-by-step.
First, let's simplify three ninths. To simplify this, we divide both the numerator and the denominator by the greatest common divisor, which is 3. This gives us 1/3.
Next, we have the quantity 1 plus the square root of 25 squared. The square root of 25 is 5, so we have 1 + 5^2. Evaluating the exponent first, we get 1 + 25 = 26.
Now, let's simplify the quantity five minus one cubed. The expression inside the parentheses, five minus one, is equal to 4. Cubing 4 gives us 4^3 = 64.
Now, let's substitute these simplified values back into the original expression:
1/3 * 26 - 64
Multiplying 1/3 by 26 gives us 26/3.
So, the simplified expression is 26/3 - 64.
To simplify this, we need to find a common denominator for 3 and 1. The common denominator is 3, so we rewrite 64 as 192/3.
Now we subtract the two fractions:
26/3 - 192/3 = -166/3
Therefore, the simplified expression is -166/3.
However, none of the answer choices match this result, so there may be a mistake in the original question or the answer choices.
To simplify this expression, let's break it down step by step.
First, let's simplify the expression within the parentheses "5 − 1." This gives us 4.
Next, let's evaluate the expression inside the square root "1 + √25." The square root of 25 is 5, so 1 + 5 equals 6.
Now, we can square this value of 6. 6 squared equals 36.
Moving on to the numerator, let's simplify the fraction "3/9." Both 3 and 9 can be divided by 3, resulting in 1/3.
Multiplying the numerator and denominator, we have (1/3) * 36.
Simplifying this further, we get 36/3, which is equal to 12.
Finally, let's evaluate "12 − 4" which gives us 8.
Thus, the answer is c) 8.