Question

How do I solve this?

Answer 1

`(175-172)/((29 )/(√(20) ) ) = (3)/((29)/(√(20) ) ) =(3√(20) )/(29)=\boxed{(6√(5) )/(29) } = \boxed{0.463}`

Refer to the attached image for further explanation:

Answer 2

Hi there! Hopefully this helps!

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Answer:
`\boxed{(6√(5) )/(29) = 0.462634754 }`

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`(175-172)/((29)/(√(20) ) )`

Subtract 172 from 175 to get 3.

`(3)/((29)/(√(20) ) )` ≈ 0.462634754

Factor
`20=2^(2) * 5`. Rewrite the square root of the product
`\sqrt{2^(2) * 5 }` ≈
`4.472135955` as the product of square roots
`\sqrt{2^(2) } √(5)` ≈ 4.472135955. Take the square root of
`2^(2)` ≈
`4`

`(3)/((29)/(2√(5) ) )`

Rationalize the denominator of
`(29)/(2√(5) )` ≈
`6.484597135` by multiplying numerator and denominator by
`√(5)` ≈
`2.236067977.`

`(3)/((29√(5) )/(2(√(5) )^(2) ) )`

The square of
`√(5)` ≈
`2.236067977` is 5.

`(3)/((29√(5) )/(2 * 5 ) )` ≈
`0.462634754`

Multiply 2 and 5 to get 10.

`(3)/((29√(5) )/(10 ) )` ≈
`0.462634754`

Divide 3 by
`(29√(5) )/(10)` ≈ 6.484597135 by multiplying 3 by the reciprocal of
`(29√(5) )/(10)` ≈
`6.484597135.`

`(3* 10)/(29√(5) )` ≈
`0.462634754`

Rationalize the denominator of
`(3* 10)/(29√(5) )` ≈ 0.462634754 by multiplying numerator and denominator by
`√(5)` ≈
`2.236067977.`

`(3* 10√(5) )/(29(√(5))^(2) )` ≈
`0.462634754`

The square of
`√(5)` ≈
`2.236067977` is 5.

`\frac{3* 10√(5) }{29 * {5} }` ≈
`0.462634754`

Multiply 3 and 10 to get 30.

`\frac{30√(5) }{29 * {5} }` ≈
`0.462634754`

Multiply 29 and 5 to get 145.

`(30√(5) )/(145 )` ≈
`0.462634754`

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Divide
`30√(5)` ≈
`67.082039325` by 145 to get, you guessed it,
`(6)/(29)√(5)` ≈
`0.462634754.`