Answer:
1) [tex]\frac{18}{7}[/tex]
2) [tex]\frac{175\sqrt{3}}{18}[/tex]
Step-by-step explanation:
* Lets explain how to simplify a square root
1)
∵ [tex]2\sqrt{21}[/tex] × [tex]\sqrt{27}[/tex] ÷ [tex]\sqrt{343}[/tex]
∵ [tex]\sqrt{21}=\sqrt{3}[/tex] × [tex]\sqrt{7}[/tex]
∴ [tex]2\sqrt{21}[/tex] = [tex]2\sqrt{3}[/tex] × [tex]\sqrt{7}[/tex]
∵ [tex]\sqrt{27}[/tex] = [tex]\sqrt{3}[/tex] × [tex]\sqrt{3}[/tex] × [tex]\sqrt{3}[/tex]
∵ [tex]\sqrt{3}[/tex] × [tex]\sqrt{3}[/tex] = 3
∴ [tex]\sqrt{27}[/tex] = [tex]3\sqrt{3}[/tex]
∴ [tex]2\sqrt{21}[/tex] × [tex]\sqrt{27}[/tex] =
[tex]2\sqrt{3}[/tex] × [tex]\sqrt{7}[/tex] × [tex]3\sqrt{3}[/tex]
∵ [tex]\sqrt{3}[/tex] × [tex]\sqrt{3}[/tex] = 3
∵ 2 × 3 × 3 = 18
∴ [tex]2\sqrt{21}[/tex] × [tex]\sqrt{27}[/tex] = [tex]18\sqrt{7}[/tex]
∵ [tex]\sqrt{343}[/tex] = [tex]\sqrt{7}[/tex] × [tex]\sqrt{7}[/tex] × [tex]\sqrt{7}[/tex]
∵ [tex]\sqrt{7}[/tex] × [tex]\sqrt{7}[/tex] = 7
∴ [tex]\sqrt{343}[/tex] = [tex]7\sqrt{7}[/tex]
∵ [tex]2\sqrt{21}[/tex] × [tex]\sqrt{27}[/tex] ÷ [tex]\sqrt{343}[/tex] =
[tex]18\sqrt{7}[/tex] ÷ [tex]7\sqrt{7}[/tex]
∵ [tex]\sqrt{7}[/tex] ÷ [tex]\sqrt{7}[/tex] = 1
∴ [tex]2\sqrt{21}[/tex] × [tex]\sqrt{27}[/tex] ÷ [tex]\sqrt{343}[/tex] =
[tex]\frac{18}{7}[/tex]
2)
∵ [tex]7\sqrt{5}[/tex] × [tex]\sqrt{125}[/tex] ÷ [tex]2\sqrt{27}[/tex]
∵ [tex]\sqrt{125}[/tex] = [tex]\sqrt{5}[/tex] × [tex]\sqrt{5}[/tex] × [tex]\sqrt{5}[/tex]
∵ [tex]\sqrt{5}[/tex] × [tex]\sqrt{5}[/tex] = 5
∴ [tex]\sqrt{125}[/tex] = [tex]5\sqrt{5}[/tex]
∴ [tex]7\sqrt{5}[/tex] × [tex]\sqrt{125}[/tex] =
[tex]7\sqrt{5}[/tex] × [tex]5\sqrt{5}[/tex]
∵ [tex]\sqrt{5}[/tex] × [tex]\sqrt{5}[/tex] = 5
∴ [tex]7\sqrt{5}[/tex] × [tex]\sqrt{125}[/tex] = 7 × 5 × 5 = 175
∵ [tex]2\sqrt{27}[/tex] = [tex]2\sqrt{3}[/tex] × [tex]\sqrt{3}[/tex] × [tex]\sqrt{3}[/tex]
∵ [tex]\sqrt{3}[/tex] × [tex]\sqrt{3}[/tex] = 3
∴ [tex]2\sqrt{27}[/tex] = [tex]6\sqrt{3}[/tex]
∴ [tex]7\sqrt{5}[/tex] × [tex]\sqrt{125}[/tex] ÷ [tex]2\sqrt{27}[/tex] =
175 ÷ [tex]6\sqrt{3}[/tex] = [tex]\frac{175}{6\sqrt{3}}[/tex]
∵ [tex]\frac{175}{6\sqrt{3}}[/tex] not in the simplest form because
the denominator has square root
∴ Multiply up and down by [tex]\sqrt{3}[/tex]
∴ [tex]\frac{175}{6\sqrt{3}}[/tex] = [tex]\frac{175\sqrt{3}}{6\sqrt{3}*\sqrt{3}}[/tex]
∴ [tex]\frac{175}{6\sqrt{3}}[/tex] = [tex]\frac{175\sqrt{3}}{18}[/tex]
∴ [tex]7\sqrt{5}[/tex] × [tex]\sqrt{125}[/tex] ÷ [tex]2\sqrt{27}[/tex] =
[tex]\frac{175\sqrt{3}}{18}[/tex]
