Question

How do I solve this?

Answer 1

Hi there! Hopefully this helps!

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Answer: $\boxed{\frac{6\sqrt{5} }{29} = 0.462634754 }$

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

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.

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

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Divide $30\sqrt{5}$ ≈ $67.082039325$ by 145 to get, you guessed it, $\frac{6}{29}\sqrt{5}$ ≈ $0.462634754.$

Answer 2

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

Refer to the attached image for further explanation: