Find the answer to start fraction four over five end fraction square root of 175 end square root and select the correct answer below. Also, is the product of a nonzero rational number and an irrational number classified as rational or irrational?

20 square root of seven end square root comma irrational
start fraction four square root of seven end square root over five end fraction comma rational
four square root of seven end square root comma irrational
start fraction 28 square root of 25 end square root over five end fraction comma rational

Question

20-09-2021
Mathematics

contestada

Find the answer to start fraction four over five end fraction square root of 175 end square root and select the correct answer below. Also, is the product of a nonzero rational number and an irrational number classified as rational or irrational?

20 square root of seven end square root comma irrational
start fraction four square root of seven end square root over five end fraction comma rational
four square root of seven end square root comma irrational
start fraction 28 square root of 25 end square root over five end fraction comma rational

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kobenhavn kobenhavn · Answer 1 · 2021-10-02T06:04:35+02:00

The simplified from of the given expression is [tex]4\times \sqrt{7}[/tex] and the product of a nonzero rational number and an irrational number is always irrational.

So, the correct option is four square root of seven end square root comma irrational.

start fraction four over five end fraction square root of [tex]175[/tex] end square root

[tex]\frac{4}{5} \sqrt{175}[/tex]

[tex]175=5\times 5 \times 7[/tex]

[tex]=\frac{4}{5} \sqrt{5\times 5 \times 7}[/tex]

[tex]=\frac{4}{5} \times 5 \sqrt{ 7}[/tex]

[tex]=4\times \sqrt{7}[/tex]

The product of a nonzero rational number and an irrational number is always irrational.

For example: [tex]4[/tex] is a rational number and [tex]\sqrt{7}[/tex] is an irrational number but their product is irrational.

Learn more about properties of rational and irrational numbers here:

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