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Question Which 2536\frac{\sqrt{25}}{\sqrt{36}} is equivalent? A. 2536\sqrt{\frac{25}{36}} B. 2536\frac{25}{36} C. 253363\frac{\sqrt[3]{25}}{\sqrt[3]{36}} D. 56\frac{\sqrt{5}}{\sqrt{6}}

Studdy Solution

STEP 1

Assumptions
1. The square root of a number is the value that, when multiplied by itself, gives the original number.
2. The square root of a fraction is equal to the square root of the numerator divided by the square root of the denominator.
3. The square root operation is the inverse of squaring a number.

STEP 2

First, we need to simplify the given expression. We can do this by finding the square root of the numbers in the numerator and the denominator.
2536\frac{\sqrt{25}}{\sqrt{36}}

STEP 3

Now, calculate the square root of 25 and 36.
25=5\sqrt{25} = 5 36=6\sqrt{36} = 6

STEP 4

Substitute the square root values back into the original expression.
2536=56\frac{\sqrt{25}}{\sqrt{36}} = \frac{5}{6}

STEP 5

Now, let's compare the simplified expression with the given options.
Option A: 2536\sqrt{\frac{25}{36}} is equivalent to 2536\frac{\sqrt{25}}{\sqrt{36}} according to the property of square roots.
Option B: 2536\frac{25}{36} is not equivalent to 56\frac{5}{6} as the square root operation has not been applied.
Option C: 253363\frac{\sqrt[3]{25}}{\sqrt[3]{36}} is not equivalent to 56\frac{5}{6} as the cube root operation is not the same as the square root operation.
Option D: 56\frac{\sqrt{5}}{\sqrt{6}} is not equivalent to 56\frac{5}{6} as the square root operation has not been applied to the numbers 5 and 6.
Therefore, the answer is option A: 2536\sqrt{\frac{25}{36}}.

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