Given:
Part A: [tex]\sqrt{7}+\sqrt{3}+\sqrt{98}-\sqrt{18}[/tex]
Part B: [tex]3 \sqrt{5}-3 \sqrt{11}+2 \sqrt{121}-3 \sqrt{90}[/tex]
To find:
The simplified radical form.
Solution:
Part A: [tex]\sqrt{7}+\sqrt{3}+\sqrt{98}-\sqrt{18}[/tex]
[tex]\sqrt{98}=\sqrt{7^2 \times 2} =7 \sqrt{2}[/tex]
[tex]\sqrt{18}=\sqrt{3^2 \times 2} =3 \sqrt{2}[/tex]
Substitute these in the given expression.
[tex]\sqrt{7}+\sqrt{3}+\sqrt{98}-\sqrt{18}=\sqrt{7}+\sqrt{3}+7\sqrt{ 2}-3\sqrt{ 2}[/tex]
Add or subtract the coefficient of same radical.
[tex]=\sqrt{7}+\sqrt{3}+(7-3)\sqrt{ 2}[/tex]
[tex]=\sqrt{7}+\sqrt{3}+4\sqrt{ 2}[/tex]
Part B: [tex]3 \sqrt{5}-3 \sqrt{11}+2 \sqrt{121}-3 \sqrt{90}[/tex]
[tex]2 \sqrt{121}=2\sqrt{11^2}[/tex]
[tex]=2\times 11[/tex]
= 22
[tex]3 \sqrt{90}=3\sqrt{3^2 \times 10}[/tex]
[tex]=3\times 3 \sqrt{10}[/tex]
[tex]=9 \sqrt{10}[/tex]
Substitute these in the given expression.
[tex]3 \sqrt{5}-3 \sqrt{11}+2 \sqrt{121}-3 \sqrt{90}=3 \sqrt{5}-3 \sqrt{11}+22-9 \sqrt{10}[/tex]
