\sqrt{75 \dfrac{46}{49}}=

General
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\sqrt{75 \dfrac{46}{49}}=

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What is the value of (\sqrt{75 \dfrac{46}{49}})?

Answer: Let’s simplify (\sqrt{75 \frac{46}{49}}).

  1. Convert the mixed fraction to an improper fraction:

    First, express (75 \frac{46}{49}) as an improper fraction:

    [
    75 = \frac{75 \times 49}{49} = \frac{3675}{49}
    ]

    So, (75 \frac{46}{49} = \frac{3675 + 46}{49} = \frac{3721}{49}).

  2. Simplify the square root expression:

    Now, find (\sqrt{\frac{3721}{49}}):

    [
    \sqrt{\frac{3721}{49}} = \frac{\sqrt{3721}}{\sqrt{49}}
    ]

    • (\sqrt{49} = 7)
    • (\sqrt{3721} = 61) (since (61 \times 61 = 3721))

  3. Final calculation:

    [
    \frac{61}{7}
    ]

So, (\sqrt{75 \frac{46}{49}} = \frac{61}{7}).

Summary: The value of (\sqrt{75 \frac{46}{49}}) simplifies to (\frac{61}{7}).