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12)(sqrt (27)+sqrt (12))/(sqrt (45)-sqrt (5))cdot (sqrt (3))/(sqrt (5)) ipleminin A) 3 (1)/(2) (3)/(2) B (5)/(2)

Soru

12)(sqrt (27)+sqrt (12))/(sqrt (45)-sqrt (5))cdot (sqrt (3))/(sqrt (5))
ipleminin
A) 3
(1)/(2)
(3)/(2)
B (5)/(2)

12)(sqrt (27)+sqrt (12))/(sqrt (45)-sqrt (5))cdot (sqrt (3))/(sqrt (5)) ipleminin A) 3 (1)/(2) (3)/(2) B (5)/(2)

Çözüm

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Usta · 5 yıl öğretmeni
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Cevap

To solve the expression \frac{\sqrt{27} + \sqrt{12}}{\sqrt{45} - \sqrt{5}} \cdot \frac{\sqrt{3}}{\sqrt{5}}, we need to simplify each part of the expression step by step.

First, let's simplify the square roots in the numerator and denominator:

\sqrt{27} = \sqrt{9 \cdot 3} = \sqrt{9} \cdot \sqrt{3} = 3\sqrt{3}

\sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}

\sqrt{45} = \sqrt{9 \cdot 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5}

Now substitute these simplified forms back into the original expression:

\frac{3\sqrt{3} + 2\sqrt{3}}{3\sqrt{5} - \sqrt{5}} \cdot \frac{\sqrt{3}}{\sqrt{5}}

Combine like terms in the numerator and denominator:

\frac{(3\sqrt{3} + 2\sqrt{3})}{(3\sqrt{5} - \sqrt{5})} = \frac{5\sqrt{3}}{2\sqrt{5}}

Next, multiply by \frac{\sqrt{3}}{\sqrt{5}}:

\frac{5\sqrt{3}}{2\sqrt{5}} \cdot \frac{\sqrt{3}}{\sqrt{5}} = \frac{5\sqrt{3} \cdot \sqrt{3}}{2\sqrt{5} \cdot \sqrt{5}} = \frac{5 \cdot 3}{2 \cdot 5} = \frac{15}{10} = \frac{3}{2}

Thus, the correct answer is:

C) \frac{3}{2}
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