Question
Simplify \( \frac{-21+\sqrt{49}}{-7} \) without using a calculator.
Ask by Pearson Huang. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified value is 2.
Solution
We start by simplifying the square root: √49 = 7.
Then the expression becomes:
( -21 + 7 ) / ( -7 )
Simplify the numerator:
-21 + 7 = -14
Now, the fraction is:
-14 / -7
Since a negative divided by a negative is positive, we simplify:
-14 / -7 = 14 / 7 = 2
Thus, the simplified value is 2.
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Simplify this solution Bonus Knowledge
To simplify \( \frac{-21+\sqrt{49}}{-7} \), we start by calculating \( \sqrt{49} \). We know that \( \sqrt{49} = 7 \). Now substitute this back into the expression: \[ \frac{-21 + 7}{-7} \] Next, simplify the numerator: \[ -21 + 7 = -14 \] Now we have: \[ \frac{-14}{-7} \] When we divide \(-14\) by \(-7\), we get: \[ \frac{-14}{-7} = 2 \] Thus, the simplified form of the expression is: \[ \boxed{2} \]
