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

1) \frac{18}{7}

7

18

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

18

175

3

Step-by-step explanation:

* Lets explain how to simplify a square root

1)

∵ 2\sqrt{21}2

21

× \sqrt{27}

27

÷ \sqrt{343}

343

∵ \sqrt{21}=\sqrt{3}

21

=

3

× \sqrt{7}

7

∴ 2\sqrt{21}2

21

= 2\sqrt{3}2

3

× \sqrt{7}

7

∵ \sqrt{27}

27

= \sqrt{3}

3

× \sqrt{3}

3

× \sqrt{3}

3

∵ \sqrt{3}

3

× \sqrt{3}

3

= 3

∴ \sqrt{27}

27

= 3\sqrt{3}3

3

∴ 2\sqrt{21}2

21

× \sqrt{27}

27

=

2\sqrt{3}2

3

× \sqrt{7}

7

× 3\sqrt{3}3

3

∵ \sqrt{3}

3

× \sqrt{3}

3

= 3

∵ 2 × 3 × 3 = 18

∴ 2\sqrt{21}2

21

× \sqrt{27}

27

= 18\sqrt{7}18

7

∵ \sqrt{343}

343

= \sqrt{7}

7

× \sqrt{7}

7

× \sqrt{7}

7

∵ \sqrt{7}

7

× \sqrt{7}

7

= 7

∴ \sqrt{343}

343

= 7\sqrt{7}7

7

∵ 2\sqrt{21}2

21

× \sqrt{27}

27

÷ \sqrt{343}

343

=

18\sqrt{7}18

7

÷ 7\sqrt{7}7

7

∵ \sqrt{7}

7

÷ \sqrt{7}

7

= 1

∴ 2\sqrt{21}2

21

× \sqrt{27}

27

÷ \sqrt{343}

343

=

\frac{18}{7}

7

18

2)

∵ 7\sqrt{5}7

5

× \sqrt{125}

125

÷ 2\sqrt{27}2

27

∵ \sqrt{125}

125

= \sqrt{5}

5

× \sqrt{5}

5

× \sqrt{5}

5

∵ \sqrt{5}

5

× \sqrt{5}

5

= 5

∴ \sqrt{125}

125

= 5\sqrt{5}5

5

∴ 7\sqrt{5}7

5

× \sqrt{125}

125

=

7\sqrt{5}7

5

× 5\sqrt{5}5

5

∵ \sqrt{5}

5

× \sqrt{5}

5

= 5

∴ 7\sqrt{5}7

5

× \sqrt{125}

125

= 7 × 5 × 5 = 175

∵ 2\sqrt{27}2

27

= 2\sqrt{3}2

3

× \sqrt{3}

3

× \sqrt{3}

3

∵ \sqrt{3}

3

× \sqrt{3}

3

= 3

∴ 2\sqrt{27}2

27

= 6\sqrt{3}6

3

∴ 7\sqrt{5}7

5

× \sqrt{125}

125

÷ 2\sqrt{27}2

27

=

175 ÷ 6\sqrt{3}6

3

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

6

3

175

∵ \frac{175}{6\sqrt{3}}

6

3

175

not in the simplest form because

the denominator has square root

∴ Multiply up and down by \sqrt{3}

3

∴ \frac{175}{6\sqrt{3}}

6

3

175

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

6

3

∗

3

175

3

∴ \frac{175}{6\sqrt{3}}

6

3

175

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

18

175

3

∴ 7\sqrt{5}7

5

× \sqrt{125}

125

÷ 2\sqrt{27}2

27

=

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

18

175

3

choice b is correct

step-by-step explanation:

we have been given the following system of inequalities;

we are required to graph the solution to the system of inequalities. using a graphing tool, the graph of the system is as shown in the attachment. the continuous line represents the graph of while the dotted line represents .

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

hope this !