Answer:
Q1:
[tex]-5\sqrt{27c^2}[/tex]
[tex]-5\sqrt{27}\sqrt{c^2}[/tex]
[tex]-5\times\sqrt{9} \sqrt{3} \sqrt{c^2}[/tex]
[tex]-5\times3\sqrt{3}\sqrt{c^2}[/tex]
[tex]-5\times3\sqrt{3}c[/tex]
[tex]-15\sqrt{3}c[/tex]
Q2:
[tex]5\sqrt{72}-3\sqrt{32}[/tex]
[tex]5\sqrt{36} \sqrt{2} -3\sqrt{16} \sqrt{2}[/tex]
[tex]5\times6\sqrt{2}-3\times4\sqrt{2}[/tex]
[tex]30\sqrt{2}-12\sqrt{2}[/tex]
[tex]18\sqrt{2}[/tex]
Q3:
[tex]\sqrt{108yz}+3\sqrt{98yz}+2\sqrt{75yz}[/tex]
[tex]\sqrt{36} \sqrt{3} \sqrt{yz} +3\sqrt{49} \sqrt{2} \sqrt{yz} +2\sqrt{25} \sqrt{3} \sqrt{yz}[/tex]
[tex]6\sqrt{3}\sqrt{yz}+21\sqrt{2}\sqrt{yz}+10\sqrt{3}\sqrt{yz}[/tex]
[tex]16\sqrt{3}\sqrt{yz}+21\sqrt{2}\sqrt{yz}[/tex]
Q4:
[tex]\sqrt{15n^2}\sqrt{10n^3}[/tex]
[tex]\sqrt{15}n\sqrt{10n^3}[/tex]
[tex]\sqrt{15}n\sqrt{10}\sqrt{n^2}\sqrt{n}[/tex]
[tex]\sqrt{15}\sqrt{10}n^2\sqrt{n}[/tex]
[tex]\sqrt{5}\sqrt{3}\sqrt{5}\sqrt{2}n^2\sqrt{n}[/tex]
[tex]5\sqrt{3}\sqrt{2}n^2\sqrt{n}[/tex]
[tex]5\sqrt{6}n^2\sqrt{n}[/tex]
Q5:
[tex]\frac{\sqrt{3x^2y^3}}{4\sqrt{5xy^3}}[/tex]
[tex]\frac{\sqrt{3}xy\sqrt{y}}{4\sqrt{5}y\sqrt{x}\sqrt{y}}[/tex]
Cancel off [tex]\sqrt{x}[/tex]:
[tex]\frac{\sqrt{3}y\sqrt{x}\sqrt{y}}{4\sqrt{5}y\sqrt{y}}[/tex]
Cancel off [tex]y:[/tex]
[tex]\frac{\sqrt{3}\sqrt{x}\sqrt{y}}{4\sqrt{5}\sqrt{y}}[/tex]
Cancel off [tex]\sqrt{y} :[/tex]
[tex]\frac{\sqrt{3}\sqrt{x}}{4\sqrt{5}}[/tex]
Multiply [tex]\sqrt{5}[/tex] on the numerator and denominator:
[tex]\frac{\sqrt{3}\sqrt{x}\sqrt{5}}{4\sqrt{5}\sqrt{5}}[/tex]
[tex]\frac{\sqrt{15}\sqrt{x}}{20}[/tex]
