Mathematics, 16.05.2021 17:40 Luzperez09

Simplify the following ,leaving your answer as a surd
4/√5+3√125

Answers: 1

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Answer from: cheergirlkr4746

1) \frac{18}{7}

2) \frac{175\sqrt{3}}{18}

175

Step-by-step explanation:

* Lets explain how to simplify a square root

∵ 2\sqrt{21}2

× \sqrt{27}

÷ \sqrt{343}

343

∵ \sqrt{21}=\sqrt{3}

× \sqrt{7}

∴ 2\sqrt{21}2

= 2\sqrt{3}2

× \sqrt{7}

∵ \sqrt{27}

= \sqrt{3}

× \sqrt{3}

∵ \sqrt{3}

× \sqrt{3}

= 3

∴ \sqrt{27}

= 3\sqrt{3}3

∴ 2\sqrt{21}2

× \sqrt{27}

2\sqrt{3}2

× \sqrt{7}

× 3\sqrt{3}3

∵ \sqrt{3}

× \sqrt{3}

= 3

∵ 2 × 3 × 3 = 18

∴ 2\sqrt{21}2

× \sqrt{27}

= 18\sqrt{7}18

∵ \sqrt{343}

343

= \sqrt{7}

× \sqrt{7}

∵ \sqrt{7}

× \sqrt{7}

= 7

∴ \sqrt{343}

343

= 7\sqrt{7}7

∵ 2\sqrt{21}2

× \sqrt{27}

÷ \sqrt{343}

343

18\sqrt{7}18

÷ 7\sqrt{7}7

∵ \sqrt{7}

÷ \sqrt{7}

= 1

∴ 2\sqrt{21}2

× \sqrt{27}

÷ \sqrt{343}

343

\frac{18}{7}

∵ 7\sqrt{5}7

× \sqrt{125}

125

÷ 2\sqrt{27}2

∵ \sqrt{125}

125

= \sqrt{5}

× \sqrt{5}

∵ \sqrt{5}

× \sqrt{5}

= 5

∴ \sqrt{125}

125

= 5\sqrt{5}5

∴ 7\sqrt{5}7

× \sqrt{125}

125

7\sqrt{5}7

× 5\sqrt{5}5

∵ \sqrt{5}

× \sqrt{5}

= 5

∴ 7\sqrt{5}7

× \sqrt{125}

125

= 7 × 5 × 5 = 175

∵ 2\sqrt{27}2

= 2\sqrt{3}2

× \sqrt{3}

∵ \sqrt{3}

× \sqrt{3}

= 3

∴ 2\sqrt{27}2

= 6\sqrt{3}6

∴ 7\sqrt{5}7

× \sqrt{125}

125

÷ 2\sqrt{27}2

175 ÷ 6\sqrt{3}6

= \frac{175}{6\sqrt{3}}

175

∵ \frac{175}{6\sqrt{3}}

175

not in the simplest form because

the denominator has square root

∴ Multiply up and down by \sqrt{3}

∴ \frac{175}{6\sqrt{3}}

175

= \frac{175\sqrt{3}}{6\sqrt{3}*\sqrt{3}}

∗

175

∴ \frac{175}{6\sqrt{3}}

175

= \frac{175\sqrt{3}}{18}

175

∴ 7\sqrt{5}7

× \sqrt{125}

125

÷ 2\sqrt{27}2

\frac{175\sqrt{3}}{18}

175

Answer from: Quest

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Answer from: Quest

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step-by-step explanation:

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Simplify the following ,leaving your answer as a surd
4/√5+3√125...