\sqrt{75 \dfrac{46}{49}}=
What is the value of (\sqrt{75 \dfrac{46}{49}})?
Answer: Let’s simplify (\sqrt{75 \frac{46}{49}}).
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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}).
-
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))
-
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}).