Simplify the radical expression: √(81/25)
Understand the Problem
The question asks to simplify a radical expression involving a square root of a fraction. We need to find the square root of both the numerator (81) and the denominator (25) separately and then simplify the resulting fraction.
Answer
$\frac{9}{5}$
Answer for screen readers
$\frac{9}{5}$
Steps to Solve
- Separate the radical
Separate the square root of the fraction into the square root of the numerator divided by the square root of the denominator.
$$ \sqrt{\frac{81}{25}} = \frac{\sqrt{81}}{\sqrt{25}} $$
- Evaluate the numerator
Evaluate the square root of the numerator. The square root of 81 is 9 because $9 \times 9 = 81$.
$$ \sqrt{81} = 9 $$
- Evaluate the denominator
Evaluate the square root of the denominator. The square root of 25 is 5 because $5 \times 5 = 25$.
$$ \sqrt{25} = 5 $$
- Simplify the fraction
Substitute the square roots of the numerator and denominator back into the fraction.
$$ \frac{\sqrt{81}}{\sqrt{25}} = \frac{9}{5} $$
$\frac{9}{5}$
More Information
The simplified form of $\sqrt{\frac{81}{25}}$ is $\frac{9}{5}$. This fraction is already in its simplest form because 9 and 5 have no common factors other than 1. It can also be expressed as the mixed number $1\frac{4}{5}$ or the decimal $1.8$.
Tips
A common mistake might be incorrectly calculating the square root of 81 or 25. Remembering the perfect squares is important to avoid this.
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