Question

Perform the following operations and write the answers in radical form.

Answer 1

Given:

Part A: $\sqrt{7}+\sqrt{3}+\sqrt{98}-\sqrt{18}$

Part B: $3 \sqrt{5}-3 \sqrt{11}+2 \sqrt{121}-3 \sqrt{90}$

To find:

The simplified radical form.

Solution:

Part A: $\sqrt{7}+\sqrt{3}+\sqrt{98}-\sqrt{18}$

$\sqrt{98}=\sqrt{7^2 \times 2} =7 \sqrt{2}$

$\sqrt{18}=\sqrt{3^2 \times 2} =3 \sqrt{2}$

Substitute these in the given expression.

$\sqrt{7}+\sqrt{3}+\sqrt{98}-\sqrt{18}=\sqrt{7}+\sqrt{3}+7\sqrt{ 2}-3\sqrt{ 2}$

Add or subtract the coefficient of same radical.

                                    $=\sqrt{7}+\sqrt{3}+(7-3)\sqrt{ 2}$

                                    $=\sqrt{7}+\sqrt{3}+4\sqrt{ 2}$

Part B: $3 \sqrt{5}-3 \sqrt{11}+2 \sqrt{121}-3 \sqrt{90}$

$2 \sqrt{121}=2\sqrt{11^2}$

           $=2\times 11$

           = 22

$3 \sqrt{90}=3\sqrt{3^2 \times 10}$

           $=3\times 3 \sqrt{10}$

           $=9 \sqrt{10}$

Substitute these in the given expression.

$3 \sqrt{5}-3 \sqrt{11}+2 \sqrt{121}-3 \sqrt{90}=3 \sqrt{5}-3 \sqrt{11}+22-9 \sqrt{10}$