Question

if the square root of 2 =1.414, the square root of 5=2.236 and the square root of 3 =1.732 , find the value of (1) the square root of 72 + the square root of 48 (2) 1he square root of 125/64 .

please answer quickly

Answer 1

Heya dear user !!!

Here is your answer,

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Q. If the √2 = 1.414 , √5 = 2.236 and √3 = 1.732 ,find the value of -

$(1) \: \: \sqrt{72} + \sqrt{48} \\ \\ \sqrt{2 \times 2 \times 2 \times 3 \times 3} + \sqrt{2 \times 2 \times 2 \times 2 \times 3} \\ \\ 6 \sqrt{2} + 4 \sqrt{3} \\ \\ 6 \times 1.414 + 4 \times 1.732 \\ \\ 8.484 + 6.928 \\ \\ 15.412$

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$(2) \: \: \sqrt{ \frac{125}{64} } \\ \\ \frac{ \sqrt{125} }{ \sqrt{64} } \\ \\ \frac{ \sqrt{5 \times 5 \times 5} }{ \sqrt{8 \times 8} } \\ \\ \frac{5 \sqrt{5} }{8} \\ \\ \frac{5 \times 2.236}{8} \\ \\ \frac{11.180}{8} \\ \\ 1.3975$

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Hence,

$(1) \: \: \sqrt{72} + \sqrt{48} = 15.412 \\ \\ (2) \: \: \sqrt{ \frac{125}{64} } = 1.3975$

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Hope it helps.

Answer 2

Hey friend,
Here is the answer you were looking for:
$(1) \: \sqrt{72} + \sqrt{48} \\ \\ by \: splitting \: \\ \\ = \sqrt{2 \times 2 \times 2 \times 3 \times 3} + \sqrt{2 \times 2 \times 2 \times 2 \times 3} \\ \\ = 2 \times3 \sqrt{2} + 2 \times 2 \sqrt{3} \\ \\ = 6 \sqrt{2} + 4 \sqrt{3} \\ \\ putting \: the \: values \\ \\ = 6 \times 1.414 + 4 \times 1.732 \\ \\ = 8.848 + 6.928 \\ \\ = 15.776 \\ \\ \\ \\ (2) \: \sqrt{ \frac{125}{64} } \\ \\ = \sqrt{ \frac{ 5 \times 5 \times 5 }{8 \times 8} } \\ \\ = \frac{5 \sqrt{5} }{8} \\ \\ putting \: the \: value \\ \\ = \frac{5 \times 2.236}{8} \\ \\ = \frac{11.18}{8} \\ \\ = 1.397 \: \: (approx)$


Hope this helps!!!

@Mahak24

Thanks...
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