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Elena L [17]
3 years ago
9

How do I solve this?

Mathematics
2 answers:
Fed [463]3 years ago
6 0

Hi there! Hopefully this helps!

------------------------------------------------------------------------------------------------------

<h2>Answer: \boxed{\frac{6\sqrt{5} }{29} = 0.462634754 }</h2><h2 /><h2>~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~</h2>

\frac{175-172}{\frac{29}{\sqrt{20} } }

Subtract 172 from 175 to get 3.

\frac{3}{\frac{29}{\sqrt{20} } } ≈ 0.462634754

Factor 20=2^{2} \times 5. Rewrite the square root of the product \sqrt{2^{2} \times 5 } ≈ 4.472135955 as the product of square roots \sqrt{2^{2} } \sqrt{5} ≈ 4.472135955. Take the square root of 2^{2} ≈ 4

\frac{3}{\frac{29}{2\sqrt{5} } }

Rationalize the denominator of \frac{29}{2\sqrt{5} } ≈ 6.484597135 by multiplying numerator and denominator by \sqrt{5} ≈ 2.236067977.

\frac{3}{\frac{29\sqrt{5} }{2(\sqrt{5} )^{2} } }

The square of \sqrt{5} ≈ 2.236067977 is 5.

\frac{3}{\frac{29\sqrt{5} }{2 \times 5 } } ≈ 0.462634754

Multiply 2 and 5 to get 10.

\frac{3}{\frac{29\sqrt{5} }{10 } } ≈ 0.462634754

Divide 3 by \frac{29\sqrt{5} }{10} ≈ 6.484597135 by multiplying 3 by the reciprocal of \frac{29\sqrt{5} }{10} ≈ 6.484597135.

\frac{3\times 10}{29\sqrt{5} } ≈ 0.462634754

Rationalize the denominator of \frac{3\times 10}{29\sqrt{5} } ≈ 0.462634754 by multiplying numerator and denominator by \sqrt{5} ≈ 2.236067977.

\frac{3\times 10\sqrt{5} }{29(\sqrt{5})^{2}  } ≈ 0.462634754

The square of \sqrt{5} ≈ 2.236067977 is 5.

\frac{3\times 10\sqrt{5} }{29 \times {5}  } ≈ 0.462634754

Multiply 3 and 10 to get 30.

\frac{30\sqrt{5} }{29 \times {5}  } ≈ 0.462634754

Multiply 29 and 5 to get 145.

\frac{30\sqrt{5} }{145  } ≈ 0.462634754

<h2>~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~</h2><h2>Divide 30\sqrt{5} ≈ 67.082039325 by 145 to get, you guessed it, \frac{6}{29}\sqrt{5} ≈ 0.462634754.</h2>
Jet001 [13]3 years ago
6 0

\frac{175-172}{\frac{29 }{\sqrt{20} } } = \frac{3}{\frac{29}{\sqrt{20} } } =\frac{3\sqrt{20} }{29}=\boxed{\frac{6\sqrt{5} }{29} } = \boxed{0.463}

Refer to the attached image for further explanation:

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