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
